المؤلفون: Echarroudi, Younes

مصطلحات موضوعية: keyword:degenerate population dynamics model, keyword:Lotka-Volterra system, keyword:Carleman estimate, keyword:observability inequality, keyword:null controllability, msc:35J70, msc:45K05, msc:92D25, msc:93B05, msc:93B07

وصف الملف: application/pdf

Relation: mr:MR4628617; zbl:Zbl 07729581; reference:[1] Ainseba, B.: Exact and approximate controllability of the age and space population dynamics structured model.J. Math. Anal. Appl. 275 (2002), 562-574. Zbl 1005.92023, MR 1943766, 10.1016/S0022-247X(02)00238-X; reference:[2] Ainseba, B.: Corrigendum to ``Exact and approximate controllability of the age and space population dynamics structured model'' (J. Math. Anal. Appl. 275 (2) (2002), 562-574).J. Math. Anal. Appl. 393 (2012), 328. Zbl 1260.92095, MR 2921673, 10.1016/j.jmaa.2012.01.059; reference:[3] Ainseba, B., Aniţa, S.: Local exact controllability of the age-dependent population dynamics with diffusion.Abstr. Appl. Anal. 6 (2001), 357-368. Zbl 0995.93008, MR 1880930, 10.1155/S108533750100063X; reference:[4] Ainseba, B., Aniţa, S.: Internal exact controllability of the linear population dynamics with diffusion.Electron. J. Differ. Equ. 2004 (2004), Article ID 112, 11 pages. Zbl 1134.93311, MR 2108883; reference:[5] Ainseba, B., Aniţa, S.: Internal stabilizability for a reaction-diffusion problem modeling a predator-prey system.Nonlinear Anal., Theory Methods Appl., Ser. A 61 (2005), 491-501. Zbl 1072.35090, MR 2126609, 10.1016/j.na.2004.09.055; reference:[6] Ainseba, B., Echarroudi, Y., Maniar, L.: Null controllability of a population dynamics with degenerate diffusion.Differ. Integral Equ. 26 (2013), 1397-1410. Zbl 1313.35193, MR 3129015; reference:[7] Ainseba, B., Langlais, M.: On a population dynamics control problem with age dependence and spatial structure.J. Math. Anal. Appl. 248 (2000), 455-474. Zbl 0964.93045, MR 1776023, 10.1006/jmaa.2000.6921; reference:[8] Hassi, E. M. Ait Ben, Khodja, F. Ammar, Hajjaj, A., Maniar, L.: Null controllability of degenerate parabolic cascade systems.Port. Math. (N.S.) 68 (2011), 345-367. Zbl 1231.35103, MR 2832802, 10.4171/PM/1895; reference:[9] Alabau-Boussouira, F., Cannarsa, P., Fragnelli, G.: Carleman estimates for degenerate parabolic operators with applications to null controllability.J. Evol. Equ. 6 (2006), 161-204. Zbl 1103.35052, MR 2227693, 10.1007/s00028-006-0222-6; reference:[10] Aniţa, S.: Analysis and Control of Age-Dependent Population Dynamics.Mathematical Modelling: Theory and Applications 11. Kluwer Acadamic, Dordrecht (2000). Zbl 0960.92026, MR 1797596, 10.1007/978-94-015-9436-3; reference:[11] Apreutesei, N., Dimitriu, G.: On a prey-predator reaction-diffusion system with Holling type III functional response.J. Comput. Appl. Math. 235 (2010), 366-379. Zbl 1205.65274, MR 2677695, 10.1016/j.cam.2010.05.040; reference:[12] Barbu, V., Iannelli, M., Martcheva, M.: On the controllability of the Lotka-McKendrick model of population dynamics.J. Math. Anal. Appl. 253 (2001), 142-165. Zbl 0961.92024, MR 1804594, 10.1006/jmaa.2000.7075; reference:[13] Boutaayamou, I., Echarroudi, Y.: Null controllability of population dynamics with interior degeneracy.Electron. J. Differ. Equ. 2017 (2017), Article ID 131, 21 pages. Zbl 1370.35183, MR 3665593; reference:[14] Boutaayamou, I., Fragnelli, G.: A degenerate population system: Carleman estimates and controllability.Nonlinear Anal., Theory Methods Appl., Ser. A 195 (2020), Article ID 111742, 29 pages. Zbl 1435.35398, MR 4052601, 10.1016/j.na.2019.111742; reference:[15] Boutaayamou, I., Salhi, J.: Null controllability for linear parabolic cascade systems with interior degeneracy.Electron. J. Differ. Equ. 2016 (2016), Article ID 305, 22 pages. Zbl 1353.35184, MR 3604750; reference:[16] Cabello, T., Gámez, M., Varga, Z.: An improvement of the Holling type III functional response in entomophagous species model.J. Biol. Syst. 15 (2007), 515-524. Zbl 1146.92326, 10.1142/S0218339007002325; reference:[17] Campiti, M., Metafune, G., Pallara, D.: Degenerate self-adjoint evolution equations on the unit interval.Semigroup Forum 57 (1998), 1-36. Zbl 0915.47029, MR 1621852, 10.1007/PL00005959; reference:[18] Cannarsa, P., Fragnelli, G.: Null controllability of semilinear degenerate parabolic equations in bounded domains.Electron. J. Differ. Equ. 2006 (2006), Article ID 136, 20 pages. Zbl 1112.35335, MR 2276561; reference:[19] Cannarsa, P., Fragnelli, G., Rocchetti, D.: Null controllability of degenerate parabolic with drift.Netw. Heterog. Media 2 (2007), 695-715. Zbl 1140.93011, MR 2357764, 10.3934/nhm.2007.2.695; reference:[20] Cannarsa, P., Fragnelli, G., Rocchetti, D.: Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form.J. Evol. Equ. 8 (2008), 583-616. Zbl 1176.35108, MR 2460930, 10.1007/s00028-008-0353-34; reference:[21] Cannarsa, P., Fragnelli, G., Vancostenoble, J.: Linear degenerate parabolic equations in bounded domains: Controllability and observability.Systems, Control, Modeling and Optimization IFIP International Federation for Information Processing 202. Springer, New York (2006), 163-173. Zbl 1214.93021, MR 2241704, 10.1007/0-387-33882-9_15; reference:[22] Cannarsa, P., Fragnelli, G., Vancostenoble, J.: Regional controllability of semilinear degenerate parabolic equations in bounded domains.J. Math. Anal. Appl. 320 (2006), 804-818. Zbl 1177.93016, MR 2225996, 10.1016/j.jmaa.2005.07.006; reference:[23] Cannarsa, P., Martinez, P., Vancostenoble, J.: Persistent regional null controllability for a class of degenerate parabolic equations.Commun. Pure Appl. Anal. 3 (2004), 607-635. Zbl 1063.35092, MR 2106292, 10.3934/cpaa.2004.3.607; reference:[24] Cannarsa, P., Martinez, P., Vancostenoble, J.: Null controllability of degenerate heat equations.Adv. Differ. Equ. 10 (2005), 153-190. Zbl 1145.35408, MR 2106129; reference:[25] Dawes, J. H. P., Souza, M. O.: A derivation of Holling's type I, II and III functional responses in predator-prey systems.J. Theor. Biol. 327 (2013), 11-22. Zbl 1322.92056, MR 3046076, 10.1016/j.jtbi.2013.02.017; reference:[26] Echarroudi, Y., Maniar, L.: Null controllability of a model in population dynamics.Electron. J. Differ. Equ. 2014 (2014), Article ID 240, 20 pages. Zbl 06430755, MR 3291740; reference:[27] Echarroudi, Y., Maniar, L.: Null controllability of a degenerate cascade model in population dynamics.Studies in Evolution Equations and Related Topics STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham (2021), 211-268. Zbl 07464638, MR 4367456, 10.1007/978-3-030-77704-3_10; reference:[28] Fragnelli, G.: An age-dependent population equation with diffusion and delayed birth process.Int. J. Math. Math. Sci. 2005 (2005), 3273-3289. Zbl 1084.92029, MR 2208054, 10.1155/IJMMS.2005.3273; reference:[29] Fragnelli, G.: Null controllability of degenerate parabolic equations in non divergence form via Carleman estimates.Discrete Contin. Dyn. Syst., Ser. S 6 (2013), 687-701. Zbl 1258.93025, MR 3010677, 10.3934/dcdss.2013.6.687; reference:[30] Fragnelli, G.: Carleman estimates and null controllability for a degenerate population model.J. Math. Pures Appl. (9) 115 (2018), 74-126. Zbl 1391.35238, MR 3808342, 10.1016/j.matpur.2018.01.003; reference:[31] Fragnelli, G.: Null controllability for a degenerate population model in divergence form via Carleman estimates.Adv. Nonlinear Anal. 9 (2020), 1102-1129. Zbl 1427.35141, MR 4019739, 10.1515/anona-2020-0034; reference:[32] Fragnelli, G., Idrissi, A., Maniar, L.: The asymptotic behavior of a population equation with diffusion and delayed birth process.Discrete Contin. Dyn. Syst., Ser. B 7 (2007), 735-754. Zbl 1211.35046, MR 2291870, 10.3934/dcdsb.2007.7.735; reference:[33] Fragnelli, G., Martinez, P., Vancostenoble, J.: Qualitative properties of a population dynamics system describing pregnancy.Math. Models Methods Appl. Sci. 15 (2005), 507-554. Zbl 1092.92037, MR 2137524, 10.1142/S0218202505000455; reference:[34] Fragnelli, G., Mugnai, D.: Carleman estimates and observability inequalities for parabolic equations with interior degeneracy.Adv. Nonlinear Anal. 2 (2013), 339-378. Zbl 1282.35101, MR 3199737, 10.1515/anona-2013-0015; reference:[35] Fragnelli, G., Mugnai, D.: Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations.Mem. Am. Math. Soc. 1146 (2016), 88 pages. Zbl 1377.93043, MR 3498150, 10.1090/memo/1146; reference:[36] Fragnelli, G., Tonetto, L.: A population equation with diffusion.J. Math. Anal. Appl. 289 (2004), 90-99. Zbl 1109.34042, MR 2020529, 10.1016/j.jmaa.2003.08.047; reference:[37] Fursikov, A. V., Imanuvilov, O. Y.: Controllability of Evolutions Equations.Lecture Notes Series, Seoul 34. Seoul National University, Seoul (1996). Zbl 0862.49004, MR 1406566; reference:[38] Hajjaj, A., Maniar, L., Salhi, J.: Carleman estimates and null controllability of degenerate/singular parabolic systems.Electron. J. Differ. Equ. 2016 (2016), Article ID 292, 25 pages. Zbl 1353.35186, MR 3578313; reference:[39] Hegoburu, N., Tucsnak, M.: Null controllability of the Lotka-Mckendrick system with spatial diffusion.Math. Control Relat. Fields 8 (2018), 707-720. Zbl 1417.92131, MR 3917460, 10.3934/mcrf.2018030; reference:[40] Jia, Y., Wu, J., Xu, H.-K.: Positive solutions of a Lotka-Volterra competition model with cross-diffusion.Comput. Math. Appl. 68 (2014), 1220-1228. Zbl 1367.92129, MR 3272537, 10.1016/j.camwa.2014.08.016; reference:[41] Juska, A., Gouveia, L., Gabriel, J., Koneck, S.: Negotiating bacteriological meat contamination standards in the US: The case of $\it E. Coli$ O157:H7.Sociologia Ruralis 40 (2000), 249-271. 10.1111/1467-9523.00146; reference:[42] Kooij, R. E., Zegeling, A.: A predator-prey model with Ivlev's functional response.J. Math. Anal. Appl. 198 (1996), 473-489. Zbl 0851.34030, MR 1376275, 10.1006/jmaa.1996.0093; reference:[43] Langlais, M.: A nonlinear problem in age-dependent population diffusion.SIAM J. Math. Anal. 16 (1985), 510-529. Zbl 0589.92013, MR 0783977, 10.1137/0516037; reference:[44] Liu, B., Zhang, Y., Chen, L.: Dynamics complexities of a Holling I predator-prey model concerning periodic biological and chemical control.Chaos Solitons Fractals 22 (2004), 123-134. Zbl 1058.92047, MR 2057553, 10.1016/j.chaos.2003.12.060; reference:[45] Liu, X., Huang, Q.: The dynamics of a harvested predator-prey system with Holling type IV functional response.Biosystems 169-170 (2018), 26-39. 10.1016/j.biosystems.2018.05.005; reference:[46] Mozorov, A. Y.: Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling.J. Theor. Biol. 265 (2010), 45-54. Zbl 1406.92676, MR 2981553, 10.1016/j.jtbi.2010.04.016; reference:[47] Pavel, L.: Classical solutions in Sobolev spaces for a class of hyperbolic Lotka-Volterra systems.SIAM J. Control Optim. 51 (2013), 2132-2151. Zbl 1275.35138, MR 3053572, 10.1137/090767303; reference:[48] Peng, R., Shi, J.: Non-existence of non-constant positive steady states of two Holling type-II predator-prey systems: Strong interaction case.J. Differ. Equations 247 (2009), 866-886. Zbl 1169.35328, MR 2528495, 10.1016/j.jde.2009.03.008; reference:[49] Piazzera, S.: An age-dependent population equation with delayed birth process.Math. Methods Appl. Sci. 27 (2004), 427-439. Zbl 1038.35145, MR 2034234, 10.1002/mma.462; reference:[50] Pozio, M. A., Tesei, A.: Degenerate parabolic problems in population dynamics.Japan J. Appl. Math. 2 (1985), 351-380. MR 0839335, 10.1007/BF03167082; reference:[51] Pugliese, A., Tonetto, L.: Well-posedness of an infinite system of partial differential equations modelling parasitic infection in age-structured host.J. Math. Anal. Appl. 284 (2003), 144-164. Zbl 1039.35130, MR 1996124, 10.1016/S0022-247X(03)00295-6; reference:[52] Rhandi, A., Schnaubelt, R.: Asymptotic behaviour of a non-autonomous population equation with diffusion in $L^1$.Discrete Contin. Dyn. Syst. 5 (1999), 663-683. Zbl 1002.92016, MR 1696337, 10.3934/dcds.1999.5.663; reference:[53] Salhi, J.: Null controllability for a coupled system of degenerate/singular parabolic equations in nondivergence form.Electron. J. Qual. Theory Differ. Equ. 2018 (2018), Article ID 31, 28 pages. Zbl 1413.35269, MR 3811494, 10.14232/ejqtde.2018.1.31; reference:[54] Seo, G., DeAngelis, D. L.: A predator-prey model with a Holling type I functional response including a predator mutual interference.J. Nonlinear Sci. 21 (2011), 811-833. Zbl 1238.92049, MR 2860930, 10.1007/s00332-011-9101-6; reference:[55] Skalski, G. T., Gilliam, J. F.: Functional responses with predator interference: Viable alternatives to the Holling type II model.Ecology 82 (2001), 3083-3092. 10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2; reference:[56] Traore, O.: Null controllability of a nonlinear population dynamics problem.Int. J. Math. Math. Sci. 2006 (2006), Article ID 49279, 20 pages. Zbl 1127.93017, MR 2268531, 10.1155/IJMMS/2006/49279; reference:[57] Wang, W., Zhang, L., Wang, H., Li, Z.: Pattern formation of a predator-prey system with Ivlev-type functional response.Ecological Modelling 221 (2010), 131-140. MR 3075712, 10.1016/j.ecolmodel.2009.09.011; reference:[58] Webb, G. F.: Population models structured by age, size, and spatial position.Structured Population Models in Biology and Epidemiology Lecture Notes in Mathematics 1936. Springer, Berlin (2008), 1-49. MR 2433574, 10.1007/978-3-540-78273-5_1; reference:[59] Zhang, Y., Xu, Z., Liu, B., Chen, L.: Dynamic analysis of a Holling I predator-prey system with mutual interference concerning pest control.J. Biol. Syst. 13 (2005), 45-58. Zbl 1073.92061, 10.1142/S0218339005001392; reference:[60] Zhao, C., Wang, M., Zhao, P.: Optimal control of harvesting for age-dependent predator-prey system.Math. Comput. Modelling 42 (2005), 573-584. Zbl 1088.92063, MR 2173475, 10.1016/j.mcm.2004.07.019

الاتاحة: http://hdl.handle.net/10338.dmlcz/151764

المؤلفون: Han, Yao-Chuang, Nie, Yu-Feng, Yuan, Zhan-Bin

مصطلحات موضوعية: keyword:radiative heat transfer, keyword:existence and uniqueness, keyword:collocation-boundary element method, keyword:shadow detection, keyword:iterative nonlinear solver, msc:45K05, msc:47G10, msc:65M38, msc:65N38, msc:80A20

وصف الملف: application/pdf

Relation: mr:MR3913885; zbl:Zbl 07031678; reference:[1] Adams, M. L., Larsen, E. W.: Fast iterative methods for discrete-ordinates particle transport calculations.Progr. Nucl. Energy 40 (2002), 3-159. 10.1016/S0149-1970(01)00023-3; reference:[2] Agoshkov, V.: Boundary Value Problems for Transport Equations.Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Boston (1998). Zbl 0914.35001, MR 1638817, 10.1007/978-1-4612-1994-1; reference:[3] Altaç, Z., Tekkalmaz, M.: Benchmark solutions of radiative transfer equation for three-dimensional rectangular homogeneous media.J. Quant. Spect. Rad. Transfer 109 (2008), 587-607. 10.1016/j.jqsrt.2007.07.016; reference:[4] Altaç, Z., Tekkalmaz, M.: Exact solution of radiative transfer equation for three-dimensional rectangular, linearly scattering medium.J. Thermophys. Heat Transf. 25 (2011), 228-238. 10.2514/1.50910; reference:[5] Atkinson, K., Chandler, G.: The collocation method for solving the radiosity equation for unoccluded surfaces.J. Integral Equations Appl. 10 (1998), 253-290. Zbl 0914.65137, MR 1656533, 10.1216/jiea/1181074231; reference:[6] Atkinson, K., Chien, D. D.-K., Seol, J.: Numerical analysis of the radiosity equation using the collocation method.ETNA, Electron. Trans. Numer. Anal. 11 (2000), 94-120. Zbl 0961.65118, MR 1799026; reference:[7] Białecki, R. A., Grela, Ł.: Application of the boundary element method in radiation.Mech. Teor. Stosow. 36 (1998), 347-364. Zbl 0934.74076; reference:[8] Blobner, J., Białecki, R. A., Kuhn, G.: Boundary-element solution of coupled heat conduction-radiation problems in the presence of shadow zones.Numer. Heat Transfer, Part B 39 (2001), 451-478. 10.1080/104077901750188840; reference:[9] Chen, S.-S., Li, B.-W., Tian, X.-Y.: Chebyshev collocation spectral domain decomposition method for coupled conductive and radiative heat transfer in a 3D L-shaped enclosure.Numer. Heat Transfer, Part B 70 (2016), 215-232. 10.1080/10407790.2016.1193398; reference:[10] Cohen, M. F., Wallace, J. R.: Radiosity and Realistic Image Synthesis.Academic Press Professional, Boston (1993). Zbl 0814.68138; reference:[11] Crosbie, A. L., Schrenker, R. G.: Exact expressions for radiative transfer in a three-dimensioanl rectangular geometry.J. Quant. Spect. Rad. Transfer 28 (1982), 507-526. 10.1016/0022-4073(82)90017-6; reference:[12] Crosbie, A. L., Schrenker, R. G.: Radiative transfer in a two-dimensional rectangular medium exposed to diffuse radiation.J. Quant. Spect. Rad. Transfer 31 (1984), 339-372. 10.1016/0022-4073(84)90095-5; reference:[13] Eberwien, U., Duenser, C., Moser, W.: Efficient calculation of internal results in 2D elasticity BEM.Eng. Anal. Bound. Elem. 29 (2005), 447-453. Zbl 1182.74214, 10.1016/j.enganabound.2005.01.008; reference:[14] Emery, A. F., Johansson, O., Lobo, M., Abrous, A.: A comparative study of methods for computing the diffuse radiation viewfactors for complex structures.J. Heat Transfer 113 (1991), 413-422. 10.1115/1.2910577; reference:[15] Hansen, O.: The local behavior of the solution of the radiosity equation at the vertices of polyhedral domains in $\Bbb R^3$.SIAM J. Math. Anal. 33 (2001), 718-750. Zbl 1001.45002, MR 1871418, 10.1137/S0036141000378103; reference:[16] Howell, J. R., Mengüç, M. P., Siegel, R.: Thermal Radiation Heat Transfer.CRC Press, Boca Raton (2010). 10.1201/9781439894552; reference:[17] Hsu, P.-F., Tan, Z.: Radiative and combined-mode heat transfer within L-shaped nonhomogeneous and nongray participating media.Numer. Heat Transfer, Part A 31 (1997), 819-835. 10.1080/10407789708914066; reference:[18] Kress, R.: Linear Integral Equations.Applied Mathematical Sciences 82, Springer, New York (2014). Zbl 1328.45001, MR 3184286, 10.1007/978-1-4614-9593-2; reference:[19] Laitinen, M. T., Tiihonen, T.: Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials.Math. Methods Appl. Sci. 21 (1998), 375-392. Zbl 0958.80003, MR 1608072, 10.1002/(SICI)1099-1476(19980325)21:53.0.CO;2-U; reference:[20] Li, B. Q., Cui, X., Song, S. P.: The Galerkin boundary element solution for thermal radiation problems.Eng. Anal. Bound. Elem. 28 (2004), 881-892. Zbl 1066.80008, 10.1016/j.enganabound.2004.01.009; reference:[21] Malalasekera, W. M., James, E. H.: Radiative heat transfer calculations in three-dimensional complex geometries.ASME J. Heat Transfer 118 (1996), 225-228. 10.1115/1.2824045; reference:[22] Modest, M. F.: Radiative Heat Transfer.Academic Press, Oxford (2013). 10.1016/C2010-0-65874-3; reference:[23] Qatanani, N. A., Daraghmeh, A.: Asymptotic error analysis for the heat radiation boundary integral equation.Eur. J. Math. Sci. 2 (2013), 51-61.; reference:[24] Sun, B., Zheng, D., Klimpke, B., Yildir, B.: Modified boundary element method for radiative heat transfer analyses in emitting, absorbing and scattering media.Eng. Anal. Bound. Elem. 21 (1998), 93-104. Zbl 0936.80006, 10.1016/S0955-7997(97)00068-4; reference:[25] Tan, Z.: Radiative heat transfer in multidimensional emitting, absorbing, and anisotropic scattering media: mathematical formulation and numerical method.J. Heat Transfer 111 (1989), 141-147. 10.1115/1.3250636; reference:[26] Thynell, S. T.: The integral form of the equation of transfer in finite, two-dimensional, cylindrical media.J. Quant. Spect. Rad. Transfer 42 (1989), 117-136. 10.1016/0022-4073(89)90094-0; reference:[27] Tiihonen, T.: Stefan-Boltzmann radiation on non-convex surfaces.Math. Methods Appl. Sci. 20 (1997), 47-57. Zbl 0872.35044, MR 1429330, 10.1002/(SICI)1099-1476(19970110)20:13.0.CO;2-B; reference:[28] Trivic, D. N., Amon, C. H.: Modeling the 3-D radiation of anisotropically scattering media by two different numerical methods.Int. J. Heat Mass Transfer 51 (2008), 2711-2732. Zbl 1143.80329, 10.1016/j.ijheatmasstransfer.2007.10.015; reference:[29] Viskanta, R.: Radiation transfer and interaction of convection with radiation heat transfer.Adv. Heat Transfer 3 (1966), 175-251. Zbl 0139.23801, 10.1016/s0065-2717(08)70052-2; reference:[30] Watt, A.: Fundamentals of Three-Dimensional Computer Graphics.Addison-Wesley Publishing Company, Wokingham (1989). Zbl 0702.68099

الاتاحة: http://hdl.handle.net/10338.dmlcz/147596

المؤلفون: Li, Yu, Lin, Qun, Xie, Hehu

مصطلحات موضوعية: keyword:parallel numerical discretization, keyword:characteristics method, keyword:population balance equations, msc:35K20, msc:45K05, msc:46N40, msc:65M22, msc:65M25, msc:65Y05, msc:92D25

وصف الملف: application/pdf

Relation: mr:MR3204439; zbl:Zbl 1340.65206

الاتاحة: http://hdl.handle.net/10338.dmlcz/702940

المؤلفون: Wehbe, Charbel

مصطلحات موضوعية: keyword:Caginalp phase-field system, keyword:Dirichlet boundary conditions, keyword:well-posedness, keyword:long time behavior of solution, keyword:global attractor, keyword:exponential attractor, keyword:Maxwell-Cattaneo law, keyword:logarithmic potential, msc:35B40, msc:35B41, msc:35G30, msc:35K51, msc:35K55, msc:35Q53, msc:45K05, msc:80A20, msc:80A22, msc:92D50

وصف الملف: application/pdf

Relation: mr:MR3396470; zbl:Zbl 06486916; reference:[1] Babin, A., Nicolaenko, B.: Exponential attractors for reaction-diffusion systems in an unbounded domain.J. Dyn. Differ. Equations 7 567-590 (1995). MR 1362671, 10.1007/BF02218725; reference:[2] Brochet, D., Hilhorst, D.: Universal attractor and inertial sets for the phase field model.Appl. Math. Lett. 4 59-62 (1991). Zbl 0773.35028, MR 1136614, 10.1016/0893-9659(91)90076-8; reference:[3] Brochet, D., Hilhorst, D., Chen, X.: Finite dimensional exponential attractor for the phase field model.Appl. Anal. 49 (1993), 197-212. Zbl 0790.35052, MR 1289743, 10.1080/00036819108840173; reference:[4] Brochet, D., Hilhorst, D., Novick-Cohen, A.: Finite-dimensional exponential attractor for a model for order-disorder and phase separation.Appl. Math. Lett. 7 83-87 (1994). Zbl 0803.35076, MR 1350381, 10.1016/0893-9659(94)90118-X; reference:[5] Caginalp, G.: An analysis of a phase field model of a free boundary.Arch. Ration. Mech. Anal. 92 205-245 (1986). Zbl 0608.35080, MR 0816623, 10.1007/BF00254827; reference:[6] Caginalp, G.: The role of microscopic anisotropy in the macroscopic behavior of a phase boundary.Ann. Phys. 172 136-155 (1986). Zbl 0639.58038, MR 0912765, 10.1016/0003-4916(86)90022-9; reference:[7] Cherfils, L., Miranville, A.: Some results on the asymptotic behavior of the Caginalp system with singular potentials.Adv. Math. Sci. Appl. 17 107-129 (2007). Zbl 1145.35042, MR 2337372; reference:[8] Conti, M., Gatti, S., Miranville, A.: Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions.Discrete Contin. Dyn. Syst., Ser. S 5 485-505 (2012). Zbl 1244.35067, MR 2861821, 10.3934/dcdss.2012.5.485; reference:[9] Fabrie, P., Galusinski, C.: Exponential attractors for partially dissipative reaction system.Asymptotic Anal. 12 329-354 (1996). MR 1402980, 10.3233/ASY-1996-12403; reference:[10] Gajewski, H., Zacharias, K.: Global behaviour of a reaction-diffusion system modelling chemotaxis.Math. Nachr. 195 (1998), 77-114. Zbl 0918.35064, MR 1654677, 10.1002/mana.19981950106; reference:[11] Grasselli, M., Miranville, A., Pata, V., Zelik, S.: Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials.Math. Nachr. 280 1475-1509 (2007). Zbl 1133.35017, MR 2354975, 10.1002/mana.200510560; reference:[12] Kufner, A., John, O., Fučík, S.: Function Spaces.Monographs and Textsbooks on Mechanics of Solids and Fluids. Mechanics: Analysis. Noordhoff International Publishing, Leyden Academia, Prague (1977). MR 0482102; reference:[13] Landau, L. D., Lifschitz, E. M.: Course of Theoretical Physics. Vol. 1.Mechanics. Akademie Berlin German (1981).; reference:[14] Miranville, A.: Exponential attractors for a class of evolution equations by a decomposition method.C. R. Acad. Sci., Paris, Sér. I, Math. 328 145-150 (1999), English. Abridged French version. Zbl 1141.35340, MR 1669003; reference:[15] Miranville, A.: On a phase-field model with a logarithmic nonlinearity.Appl. Math., Praha 57 (2012), 215-229. Zbl 1265.35139, MR 2984601, 10.1007/s10492-012-0014-y; reference:[16] Miranville, A.: Some mathematical models in phase transition.Discrete Contin. Dyn. Syst., Ser. S 7 271-306 (2014). Zbl 1275.35048, MR 3109473, 10.3934/dcdss.2014.7.271; reference:[17] Miranville, A., Quintanilla, R.: A generalization of the Caginalp phase-field system based on the Cattaneo law.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71 2278-2290 (2009). Zbl 1167.35304, MR 2524435, 10.1016/j.na.2009.01.061; reference:[18] Miranville, A., Quintanilla, R.: Some generalizations of the Caginalp phase-field system.Appl. Anal. 88 877-894 (2009). Zbl 1178.35194, MR 2548940, 10.1080/00036810903042182; reference:[19] Miranville, A., Zelik, S.: Robust exponential attractors for Cahn-Hilliard type equations with singular potentials.Math. Methods Appl. Sci. 27 (2004), 545-582. Zbl 1050.35113, MR 2041814, 10.1002/mma.464; reference:[20] Miranville, A., Zelik, S.: Attractors for dissipative partial differential equations in bounded and unbounded domains.C. M. Dafermos et al. Handbook of Differential Equations: Evolutionary Equations. Vol. IV Elsevier/North-Holland Amsterdam 103-200 (2008). Zbl 1221.37158, MR 2508165; reference:[21] Temam, R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics.Applied Mathematical Sciences 68 Springer, New York (1997). Zbl 0871.35001, MR 1441312, 10.1007/978-1-4612-0645-3

الاتاحة: http://hdl.handle.net/10338.dmlcz/144313

المؤلفون: Bárta, Tomáš

مصطلحات موضوعية: keyword:viscoelasticity, keyword:integrodifferential equation, keyword:classical solution, keyword:global existence, keyword:implicit constitutive relations, msc:35A09, msc:35M33, msc:45G10, msc:45K05, msc:74D10, msc:74H20, msc:74H40

وصف الملف: application/pdf

Relation: mr:MR3193928; zbl:Zbl 06391540; reference:[1] Bulíček M., Gwiazda P., Málek J., Świerczewska-Gwiazda A.: On unsteady flows of implicitly constituted incompressible fluids.SIAM J. Math. Anal. 44 (2012), no. 4, 2756–2801. Zbl 1256.35074, MR 3023393, 10.1137/110830289; reference:[2] Dafermos C.M., Nohel J.A.: A nonlinear hyperbolic Volterra equation in viscoelasticity. Contributions to analysis and geometry (Baltimore, Md., 1980), pp. 87–116, Johns Hopkins Univ. Press, Baltimore, Md., 1981. Zbl 0588.35016, MR 0648457; reference:[3] Gripenberg G., Londen S.O., Staffans O.: Volterra integral and functional equations.Encyclopedia of Mathematics and its Applications, 34, Cambridge University Press, Cambridge, 1990. Zbl 1159.45001, MR 1050319; reference:[4] Hrusa W.J.: A nonlinear functional-differential equation in Banach space with applications to materials with fading memory.Arch. Rational Mech. Anal. 84 (1984), no. 2, 99–137. Zbl 0544.73056, MR 0713121, 10.1007/BF00252129; reference:[5] Hrusa W.J., Nohel J.A.: The Cauchy problem in one-dimensional nonlinear viscoelasticity.J. Differential Equations 59 (1985), no. 3, 388–412. Zbl 0535.35057, MR 0807854, 10.1016/0022-0396(85)90147-0; reference:[6] Hrusa W.J., Renardy M.: A model equation for viscoelasticity with a strongly singular kernel.SIAM J. Math. Anal. 19 (1988), no. 2, 257–269. Zbl 0644.73041, MR 0930025, 10.1137/0519019; reference:[7] MacCamy R.C.: A model for one-dimensional nonlinear viscoelasticity.Quart. Appl. Math. 37 (1977), 21–33. Zbl 0355.73041, MR 0478939; reference:[8] Málek J.: Mathematical properties of flows of incompressible power-law-like fluids that are described by implicit constitutive relations.Electron. Trans. Numer. Anal. 31 (2008), 110–125. Zbl 1182.35182, MR 2569596; reference:[9] Málek J., Průša P., Rajagopal K.R.: Generalizations of the Navier–Stokes fluid from a new perspective.Internat. J. Engrg. Sci. 48 (2010), no. 12, 1907–1924. Zbl 1231.76073, MR 2778752, 10.1016/j.ijengsci.2010.06.013; reference:[10] Muliana A., Rajagopal K.R., Wineman A.S.: A new class of quasi-linear models for describing the nonlinear viscoelastic response of materials.Acta Mechanica (2013), 1–15.; reference:[11] Průša V., Rajagopal K.R.: On implicit constitutive relations for materials with fading memory.Journal of Non-Newtonian Fluid Mechanics 181-182 (2012), 22–29. 10.1016/j.jnnfm.2012.06.004; reference:[12] Rajagopal K.R.: On implicit constitutive theories.Appl. Math. 48 (2003), 279–319. Zbl 1097.76009, MR 1994378, 10.1023/A:1026062615145; reference:[13] Renardy M., Hrusa W.J., Nohel J.A.: Mathematical Problems in Viscoelasticity.Pitman Monographs and Surveys in Pure and Applied Mathematics, 35, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1987. Zbl 0719.73013, MR 0919738; reference:[14] Staffans O.J.: On a nonlinear hyperbolic Volterra equation.SIAM J. Math. Anal. 11 (1980), no. 5, 793–812. Zbl 0464.45010, MR 0586908, 10.1137/0511071

الاتاحة: http://hdl.handle.net/10338.dmlcz/143804

المؤلفون: Nandi, Prasanta Kumar, Gorain, Ganesh Chandra, Kar, Samarjit

مصطلحات موضوعية: keyword:Kirchhoff equation, keyword:dissipation, keyword:vibration, keyword:stabilization, keyword:energy decay estimate, msc:35B35, msc:35L70, msc:37L15, msc:45K05

وصف الملف: application/pdf

Relation: mr:MR3183473; zbl:Zbl 06362222; reference:[1] Aassila, M., Benaissa, A.: Global existence and asymptotic behavior of solutions of mildly degenerate Kirchhoff equations with nonlinear dissipative term.Funkc. Ekvacioj, Ser. Int. 44 (2001), 309-333 French. Zbl 1145.35432, MR 1865394; reference:[2] Autuori, G., Pucci, P.: Asymptotic stability for Kirchhoff systems in variable exponent Sobolev spaces.Complex Var. Elliptic Equ. 56 (2011), 715-753. Zbl 1230.35018, MR 2832211; reference:[3] Autuori, G., Pucci, P.: Local asymptotic stability for polyharmonic Kirchhoff systems.Appl. Anal. 90 (2011), 493-514. Zbl 1223.35051, MR 2780908, 10.1080/00036811.2010.483433; reference:[4] Autuori, G., Pucci, P., Salvatori, M. C.: Asymptotic stability for anisotropic Kirchhoff systems.J. Math. Anal. Appl. 352 (2009), 149-165. Zbl 1175.35013, MR 2499894, 10.1016/j.jmaa.2008.04.066; reference:[5] Autuori, G., Pucci, P., Salvatori, M. C.: Asymptotic stability for nonlinear Kirchhoff systems.Nonlinear Anal., Real World Appl. 10 (2009), 889-909. Zbl 1167.35314, MR 2474268, 10.1016/j.nonrwa.2007.11.011; reference:[6] D'Ancona, P., Spagnolo, S.: Nonlinear perturbations of the Kirchhoff equation.Commun. Pure Appl. Math. 47 (1994), 1005-1029. Zbl 0807.35093, MR 1283880, 10.1002/cpa.3160470705; reference:[7] Gorain, G. C.: Boundary stabilization of nonlinear vibrations of a flexible structure in a bounded domain in $R^n$.J. Math. Anal. Appl. 319 (2006), 635-650. MR 2227928, 10.1016/j.jmaa.2005.06.031; reference:[8] Gorain, G. C.: Exponential energy decay estimates for the solutions of $n$-dimensional Kirchhoff type wave equation.Appl. Math. Comput. 177 (2006), 235-242. Zbl 1098.74024, MR 2234515, 10.1016/j.amc.2005.11.003; reference:[9] Komornik, V., Zuazua, E.: A direct method for the boundary stabilization of the wave equation.J. Math. Pures Appl., IX. Sér. 69 (1990), 33-54. Zbl 0636.93064, MR 1054123; reference:[10] Lasiecka, I., Ong, J.: Global solvability and uniform decays of solutions to quasilinear equation with nonlinear boundary dissipation.Commun. Partial Differ. Equations 24 (1999), 2069-2107. Zbl 0936.35031, MR 1720766, 10.1080/03605309908821495; reference:[11] Menzala, G. P.: On classical solutions of a quasilinear hyperbolic equation.Nonlinear Anal., Theory Methods Appl. 3 (1979), 613-627. Zbl 0419.35062, MR 0541872, 10.1016/0362-546X(79)90090-7; reference:[12] Mitrinović, D. S., Pečarić, J. E., Fink, A. M.: Inequalities Involving Functions and Their Integrals and Derivatives.Mathematics and Its Applications: East European Series 53 Kluwer Academic Publishers, Dordrecht (1991). Zbl 0744.26011, MR 1190927; reference:[13] Nandi, P. K., Gorain, G. C., Kar, S.: Uniform exponential stabilization for flexural vibrations of a solar panel.Appl. Math. (Irvine) 2 (2011), 661-665. MR 2910175, 10.4236/am.2011.26087; reference:[14] Narasimha, R.: Non-linear vibration of an elastic string.J. Sound Vib. 8 (1968), 134-146. Zbl 0164.26701, 10.1016/0022-460X(68)90200-9; reference:[15] Nayfeh, A. H., Mook, D. T.: Nonlinear Oscillations.Pure and Applied Mathematics. A Wiley-Interscience Publication John Wiley & Sons, New York (1979). Zbl 0418.70001, MR 0549322; reference:[16] Newman, W. G.: Global solution of a nonlinear string equation.J. Math. Anal. Appl. 192 (1995), 689-704. Zbl 0837.35095, MR 1336472, 10.1006/jmaa.1995.1198; reference:[17] Nishihara, K.: On a global solution of some quasilinear hyperbolic equation.Tokyo J. Math. 7 (1984), 437-459. Zbl 0586.35059, MR 0776949, 10.3836/tjm/1270151737; reference:[18] Nishihara, K., Yamada, Y.: On global solutions of some degenerate quasilinear hyperbolic equations with dissipative terms.Funkc. Ekvacioj, Ser. Int. 33 (1990), 151-159. Zbl 0715.35053, MR 1065473; reference:[19] Ono, K.: Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings.J. Differ. Equations 137 (1997), 273-301. Zbl 0879.35110, MR 1456598, 10.1006/jdeq.1997.3263; reference:[20] Ono, K., Nishihara, K.: On a nonlinear degenerate integro-differential equation of hyperbolic type with a strong dissipation.Adv. Math. Sci. Appl. 5 (1995), 457-476. Zbl 0842.45005, MR 1361000; reference:[21] Shahruz, S. M.: Bounded-input bounded-output stability of a damped nonlinear string.IEEE Trans. Autom. Control 41 (1996), 1179-1182. Zbl 0863.93076, MR 1407204, 10.1109/9.533679; reference:[22] Yamazaki, T.: Global solvability for the Kirchhoff equations in exterior domains of dimension larger than three.Math. Methods Appl. Sci. 27 (2004), 1893-1916. Zbl 1072.35559, MR 2092828, 10.1002/mma.530; reference:[23] Yamazaki, T.: Global solvability for the Kirchhoff equations in exterior domains of dimension three.J. Differ. Equations 210 (2005), 290-316. Zbl 1062.35045, MR 2119986, 10.1016/j.jde.2004.10.012; reference:[24] Ye, Y.: On the exponential decay of solutions for some Kirchhoff-type modelling equations with strong dissipation.Applied Mathematics 1 (2010), 529-533. 10.4236/am.2010.16070

الاتاحة: http://hdl.handle.net/10338.dmlcz/143630

المؤلفون: Prüss, Jan

مصطلحات موضوعية: msc:34G10, msc:35K20, msc:35K22, msc:35K90, msc:45K05, msc:47D05, msc:47D06

وصف الملف: application/pdf

Relation: mr:MR1981536; zbl:Zbl 1010.35064

الاتاحة: http://hdl.handle.net/10338.dmlcz/700320

المؤلفون: Jangveladze, Temur A., Kiguradze, Zurab V.

مصطلحات موضوعية: keyword:system of nonlinear integro-differential equations, keyword:magnetic field, keyword:asymptotics for large time, msc:35B40, msc:35K51, msc:35K55, msc:35Q61, msc:45K05, msc:74H40, msc:78A30

وصف الملف: application/pdf

Relation: mr:MR2737715; zbl:Zbl 1224.35189; reference:[1] Amadori, A. L., Karlsen, K. H., Chioma, C. La: Non-linear degenerate integro-partial differential evolution equations related to geometric Lévy processes and applications to backward stochastic differential equations.Stochastics Stochastics Rep. 76 (2004), 147-177. Zbl 1049.60050, MR 2060349, 10.1080/10451120410001696289; reference:[2] Chadam, J. M., Yin, H. M.: An iteration procedure for a class of integrodifferential equations of parabolic type.J. Integral Equations Appl. 2 (1990), 31-47. Zbl 0701.45004, MR 1033202, 10.1216/JIE-1989-2-1-31; reference:[3] Coleman, B. D., Gurtin, M. E.: On the stability against shear waves of steady flows of non-linear viscoelastic fluids.J. Fluid Mech. 33 (1968), 165-181. Zbl 0207.25302, 10.1017/S0022112068002430; reference:[4] Dafermos, C. M.: An abstract Volterra equation with application to linear viscoelasticity.J. Differ. Equations 7 (1970), 554-569. MR 0259670, 10.1016/0022-0396(70)90101-4; reference:[5] Dafermos, C.: Stabilizing effects of dissipation.Proc. Int. Conf. Equadiff 82, Würzburg 1982. Lect. Notes Math. Vol. 1017 (1983), 140-147. Zbl 0547.35014, MR 0726578, 10.1007/BFb0103245; reference:[6] Dafermos, C. M., Nohel, J. A.: A nonlinear hyperbolic Volterra equation in viscoelasticity. Contributions to analysis and geometry.Suppl. Am. J. Math. (1981), 87-116. MR 0648457; reference:[7] Engler, H.: Global smooth solutions for a class of parabolic integrodifferential equations.Trans. Am. Math. Soc. 348 (1996), 267-290. Zbl 0848.45002, MR 1321573, 10.1090/S0002-9947-96-01472-9; reference:[8] Engler, H.: On some parabolic integro-differential equations: Existence and asymptotics of solutions.Proc. Int. Conf. Equadiff 82, Würzburg 1982. Lect. Notes Math. Vol. 1017 (1983), 161-167. Zbl 0539.35074, MR 0726581, 10.1007/BFb0103248; reference:[9] Gordeziani, D. G., (Dzhangveladze), T. A. Jangveladze, Korshiya, T. K.: Existence and uniqueness of the solution of certain nonlinear parabolic problems.Differ. Equations 19 (1983), 887-895. MR 0708616; reference:[10] Gripenberg, G.: Global existence of solutions of Volterra integrodifferential equations of parabolic type.J. Differ. Equations 102 (1993), 382-390. Zbl 0780.45012, MR 1216735, 10.1006/jdeq.1993.1035; reference:[11] Gripenberg, G., Londen, S.-O., Staffans, O.: Volterra Integral and Functional Equations. Encyclopedia of Mathematics and Its Applications, Vol. 34.Cambridge University Press Cambridge (1990). MR 1050319; reference:[12] Gurtin, M. E., Pipkin, A. C.: A general theory of heat conduction with finite wave speeds.Arch. Ration. Mech. Anal. 31 (1968), 113-126. Zbl 0164.12901, MR 1553521, 10.1007/BF00281373; reference:[13] (Dzhangveladze), T. A. Jangvelazde: On the solvability of the first boundary value problem for a nonlinear integro-differential equation of parabolic type.Soobsch. Akad. Nauk Gruz. SSR 114 (1984), 261-264 Russian. MR 0782476; reference:[14] (Dzhangveladze), T. A. Jangveladze, Kiguradze, Z. V.: Asymptotic behavior of the solution of a nonlinear integro-differential diffusion equation.Differ. Equ. 44 (2008), 538-550. MR 2432866, 10.1134/S0012266108040083; reference:[15] (Dzhangveladze), T. A. Jangveladze, Kiguradze, Z. V.: Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance.Sib. Mat. Zh. 47 (2006), 1058-1070 Russian English translation: Sib. Math. J. 47 (2006), 867-878. MR 2266515, 10.1007/s11202-006-0095-5; reference:[16] (Dzhangveladze), T. A. Jangveladze, Kiguradze, Z. V.: Estimates of the stabilization rate as $t\rightarrow\infty$ of solutions of the nonlinear integro-differential diffusion system.Appl. Math. Inform. Mech. 8 (2003), 1-19. MR 2072736; reference:[17] (Dzhangvelazde), T. A. Jangveladze, Kiguradze, Z. V.: On the stabilization of solutions of an initial-boundary value problem for a nonlinear integro-differential equation.Differ. Equ. 43 (2007), 854-861 Translation from Differ. Uravn. 43 (2007), 833-840 Russian. MR 2383832, 10.1134/S0012266107060110; reference:[18] (Dzhangveladze), T. A. Jangveladze, Lyubimov, B. Ya., Korshiya, T. K.: Numerical solution of a class of non-isothermal diffusion problems of an electromagnetic field.Tr. Inst. Prikl. Mat. Im. I. N. Vekua 18 (1986), 5-47 Russian. MR 0897501; reference:[19] Kačur, J.: Application of Rothe's method to evolution integrodifferential equations.J. Reine Angew. Math. 388 (1988), 73-105. Zbl 0638.65098, MR 0944184; reference:[20] Landau, L. D., Lifshitz, E. M.: Electrodynamics of Continuous Media.Pergamon Press Oxford-London-New York (1960). Zbl 0122.45002, MR 0121049; reference:[21] Laptev, G.: Mathematical singularities of a problem on the penetration of a magnetic field into a substance.Zh. Vychisl. Mat. Mat. Fiz. 28 (1988), 1332-1345 Russian English translation: U.S.S.R. Comput. Math. Math. Phys. 28 (1990), 35-45. MR 0967528; reference:[22] Laptev, G.: Quasilinear parabolic equations which contains in coefficients Volterra's operator.Math. Sbornik 136 (1988), 530-545 Russian English translation: Sbornik Math. 64 (1989), 527-542. MR 0965891; reference:[23] Lions, J.-L.: Quelques méthodes de résolution des problèmes aux limites non-linéaires.Dunod/Gauthier-Villars Paris (1969), French. Zbl 0189.40603, MR 0259693; reference:[24] Long, N. T., Dinh, A. P. N.: Nonlinear parabolic problem associated with the penetration of a magnetic field into a substance.Math. Methods Appl. Sci. 16 (1993), 281-295. Zbl 0797.35099, MR 1213185, 10.1002/mma.1670160404; reference:[25] Long, N. T., Dinh, A. P. N.: Periodic solutions of a nonlinear parabolic equation associated with the penetration of a magnetic field into a substance.Comput. Math. Appl. 30 (1995), 63-78. Zbl 0834.35070, MR 1336663, 10.1016/0898-1221(95)00068-A; reference:[26] MacCamy, R. C.: An integro-differential equation with application in heat flow.Q. Appl. Math. 35 (1977), 1-19. Zbl 0351.45018, MR 0452184, 10.1090/qam/452184; reference:[27] Renardy, M., Hrusa, W. J., Nohel, J. A.: Mathematical Problems in Viscoelasticity. Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 35.Longman Scientific & Technical/John Wiley & Sons Harlow/New York (1987). MR 0919738; reference:[28] Vishik, M.: Über die Lösbarkeit von Randwertaufgaben für quasilineare parabolische Gleichungen höherer Ordnung (On solvability of the boundary value problems for higher order quasilinear parabolic equations).Mat. Sb. N. Ser. 59 (1962), 289-325 Russian.; reference:[29] Yin, H. M.: The classical solutions for nonlinear parabolic integrodifferential equations.J. Integral Equations Appl. 1 (1988), 249-263. Zbl 0671.45004, MR 0978743, 10.1216/JIE-1988-1-2-249

الاتاحة: http://hdl.handle.net/10338.dmlcz/140822

المؤلفون: Zaraï, Abderrahmane, Tatar, Nasser-eddine

مصطلحات موضوعية: keyword:Balakrishnan-Taylor damping, keyword:polynomial decay, keyword:memory term, keyword:viscoelasticity, msc:35A01, msc:35B40, msc:35L20, msc:35L70, msc:45K05, msc:74H25, msc:74K05

وصف الملف: application/pdf

Relation: mr:MR2735903; zbl:Zbl 1240.35330; reference:[1] Alabau-Boussouira, F., Cannarsa, P., Sforza, D.: Decay estimates for second order evolution equations with memory.J. Funct. Anal. 254 (5) (2008), 1342–1372. Zbl 1145.35025, MR 2386941, 10.1016/j.jfa.2007.09.012; reference:[2] Appleby, J. A. D., Fabrizio, M., Lazzari, B., Reynolds, D. W.: On exponential asymptotic stability in linear viscoelasticity.Math. Models Methods Appl. Sci. 16 (2006), 1677–1694. Zbl 1114.45003, MR 2264556, 10.1142/S0218202506001674; reference:[3] Balakrishnan, A. V., Taylor, L. W.: Distributed parameter nonlinear damping models for flight structures.Damping 89', Flight Dynamics Lab and Air Force Wright Aeronautical Labs, WPAFB, 1989.; reference:[4] Ball, J.: Remarks on blow up and nonexistence theorems for nonlinear evolution equations.Quart. J. Math. Oxford 28 (1977), 473–486. Zbl 0377.35037, MR 0473484, 10.1093/qmath/28.4.473; reference:[5] Bass, R. W., Zes, D.: Spillover, nonlinearity and flexible structures.The Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems, NASA Conference Publication 10065 (L.W.Taylor, ed.), 1991, pp. 1–14.; reference:[6] Berrimi, S., Messaoudi, S.: Existence and decay of solutions of a viscoelastic equation with a nonlinear source.Nonlinear Anal. 64 (2006), 2314–2331. Zbl 1094.35070, MR 2213903; reference:[7] Cavalcanti, M. M., Cavalcanti, V. N. Domingos, Filho, J. S. Prates, Soriano, J. A.: Existence and uniform decay rates for viscoelastic problems with nonlocal boundary damping.Differential Integral Equations 14 (1) (2001), 85–116. MR 1797934; reference:[8] Cavalcanti, M. M., Oquendo, H. P.: Frictional versus viscoelastic damping in a semilinear wave equation.SIAM J. Control Optim. (electronic) 42 (4) (2003), 1310–1324. Zbl 1053.35101, MR 2044797, 10.1137/S0363012902408010; reference:[9] Clark, H. R.: Elastic membrane equation in bounded and unbounded domains.Electron. J. Qual. Theory Differ. Equ. 11 (2002), 1–21. Zbl 1032.35039, MR 1918508; reference:[10] Glassey, R. T.: Blow-up theorems for nonlinear wave equations.Math. Z. 132 (1973), 183–203. Zbl 0247.35083, MR 0340799, 10.1007/BF01213863; reference:[11] Haraux, A., Zuazua, E.: Decay estimates for some semilinear damped hyperbolic problems.Arch. Rational Mech. Anal. 100 (1988), 191–206. Zbl 0654.35070, MR 0913963, 10.1007/BF00282203; reference:[12] Kalantarov, V. K., Ladyzhenskaya, O. A.: The occurrence of collapse for quasilinear equations of parabolic and hyperbolic type.J. Soviet Math. 10 (1978), 53–70. 10.1007/BF01109723; reference:[13] Kirchhoff, G.: Vorlesungen über Mechanik.Tauber, Leipzig, 1883.; reference:[14] Komornik, V.: Exact controllability and stabilization. The multiplier method.RAM: Research in Applied Mathematics, Masson, Paris; John Wiley & Sons, Ltd., Chichester, 1994. Zbl 0937.93003, MR 1359765; reference:[15] Kopackova, M.: Remarks on bounded solutions of a semilinear dissipative hyperbolic equation.Comment. Math. Univ. Carolin. 30 (1989), 713–719. Zbl 0707.35026, MR 1045899; reference:[16] Li, M. R., Tsai, L. Y.: Existence and nonexistence of global solutions of some systems of semilinear wave equations.Nonlinear Anal. 54 (2003), 1397–1415. MR 1997226; reference:[17] Matsuyama, T., Ikehata, R.: On global solutions and energy decay for the wave equation of Kirchhoff type with nonlinear damping terms.J. Math. Anal. Appl. 204 (3) (1996), 729–753. MR 1422769, 10.1006/jmaa.1996.0464; reference:[18] Medjden, M., e. Tatar, N.: On the wave equation with a temporal nonlocal term.Dynam. Systems Appl. 16 (2007), 665–672. MR 2370149; reference:[19] Nakao, M.: Decay of solutions of some nonlinear evolution equation.J. Math. Anal. Appl. 60 (1977), 542–549. MR 0499564, 10.1016/0022-247X(77)90040-3; reference:[20] Nishihara, K., Yamada, Y.: On global solutions of some degenerate quasilinear hyperbolic equations with dissipative terms.Funkcial. Ekvac. 33 (1990), 151–159. Zbl 0715.35053, MR 1065473; reference:[21] Ono, K.: Global existence, decay and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings.J. Differential Equations 137 (2) (1997), 273–301. Zbl 0879.35110, MR 1456598, 10.1006/jdeq.1997.3263; reference:[22] Ono, K.: On global existence, asymptotic stability and blowing up of solutions for some degenerate nonlinear wave equations of Kirchhoff type with a strong dissipation.Math. Methods Appl. Sci. 20 (1997), 151–177. Zbl 0878.35081, MR 1430038, 10.1002/(SICI)1099-1476(19970125)20:23.0.CO;2-0; reference:[23] Ono, K.: On global solutions and blow-up solutions of nonlinear Kirchhoff strings with nonlinear dissipation.J. Math. Anal. Appl. 216 (1997), 321–342. Zbl 0893.35078, MR 1487267, 10.1006/jmaa.1997.5697; reference:[24] Pata, V.: Exponential stability in linear viscoelasticity.Quart. Appl. Math. 64 (3) (2006), 499–513. Zbl 1117.35052, MR 2259051; reference:[25] Tatar, N-e. and Zaraï, A., : Exponential stability and blow up for a problem with Balakrishnan-Taylor damping.to appear in Demonstratio Math.; reference:[26] Tatar, N-e. and Zaraï, A., : On a Kirchhoff equation with Balakrishnan-Taylor damping and source term.to apper in DCDIS.; reference:[27] You, Y.: Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan-Taylor damping.Abstr. Appl. Anal. 1 (1) (1996), 83–102. Zbl 0940.35036, MR 1390561, 10.1155/S1085337596000048

الاتاحة: http://hdl.handle.net/10338.dmlcz/140784

المؤلفون: Chen, Yujuan

مصطلحات موضوعية: keyword:strongly coupled, keyword:degenerate parabolic system, keyword:nonlocal source, keyword:global existence, keyword:blow-up, msc:35D55, msc:35K05, msc:35K59, msc:35K65, msc:45K05

وصف الملف: application/pdf

Relation: mr:MR2672409; zbl:Zbl 1224.35157; reference:[1] Anderson, J. R., Deng, K.: Global existence for degenerate parabolic equations with a non-local forcing.Math. Methods Appl. Sci. 20 (1997), 1069-1087. Zbl 0883.35066, MR 1465394, 10.1002/(SICI)1099-1476(19970910)20:133.0.CO;2-Y; reference:[2] Chen, H. W.: Analysis of blow-up for a nonlinear degenerate parabolic equation.J. Math. Anal. Appl. 192 (1995), 180-193. MR 1329419, 10.1006/jmaa.1995.1166; reference:[3] Chen, Y., Gao, H.: Asymptotic blow-up behavior for a nonlocal degenerate parabolic equation.J. Math. Anal. Appl. 330 (2007), 852-863. Zbl 1113.35100, MR 2308412, 10.1016/j.jmaa.2006.08.014; reference:[4] Deng, W., Li, Y., Xie, C.: Existence and nonexistence of global solutions of some nonlocal degenerate parabolic equations.Appl. Math. Lett. 16 (2003), 803-808. Zbl 1059.35066, MR 1986054, 10.1016/S0893-9659(03)80118-0; reference:[5] Deng, W., Li, Y., Xie, C.: Global existence and nonexistence for a class of degenerate parabolic systems.Nonlinear Anal., Theory Methods Appl. 55 (2003), 233-244. Zbl 1032.35077, MR 2007471, 10.1016/S0362-546X(03)00226-8; reference:[6] Duan, Z. W., Deng, W., Xie, C.: Uniform blow-up profile for a degenerate parabolic system with nonlocal source.Comput. Math. Appl. 47 (2004), 977-995. MR 2060331, 10.1016/S0898-1221(04)90081-8; reference:[7] Duan, Z. W., Zhou, L.: Global and blow-up solutions for nonlinear degenerate parabolic systems with crosswise-diffusion.J. Math. Anal. Appl. 244 (2000), 263-278. Zbl 0959.35100, MR 1753038, 10.1006/jmaa.1999.6665; reference:[8] Friedman, A., Mcleod, B.: Blow-up of positive solutions of semilinear heat equations.Indiana Univ. Math. J. 34 (1985), 425-447. Zbl 0576.35068, MR 0783924, 10.1512/iumj.1985.34.34025; reference:[9] Friedman, A., Mcleod, B.: Blow-up of solutions of nonlinear degenerate parabolic equations.Arch. Ration. Mech. Appl. 96 (1987), 55-80. MR 0853975, 10.1007/BF00251413; reference:[10] Gage, M. E.: On the size of the blow-up set for a quasilinear parabolic equation.Contemp. Math. 127 (1992), 41-58. Zbl 0770.35029, MR 1155408, 10.1090/conm/127/1155408; reference:[11] Ladyzenskaya, O. A., Solonnikov, V. A., Ural'tseva, N. N.: Linear and Quasilinear Equations of Parabolic Type.American Mathematical Society Providence (1968).; reference:[12] Pao, C. V.: Nonlinear Parabolic and Elliptic Equations.Plenum Press New York (1992). Zbl 0777.35001, MR 1212084; reference:[13] Passo, R. Dal, Luckhaus, S.: A degenerate diffusion problem not in divergence form.J. Differ. Equations 69 (1987), 1-14. MR 0897437, 10.1016/0022-0396(87)90099-4; reference:[14] Wang, M. X.: Some degenerate and quasilinear parabolic systems not in divergence form.J. Math. Anal. Appl. 274 (2002), 424-436. Zbl 1121.35321, MR 1936706, 10.1016/S0022-247X(02)00347-5; reference:[15] Wang, M. X., Xie, C. H.: A degenerate and strongly coupled quasilinear parabolic system not in divergence form.Z. Angew. Math. Phys. 55 (2004), 741-755. Zbl 1181.35132, MR 2087763, 10.1007/s00033-004-1133-4; reference:[16] Wang, S., Wang, M. X., Xie, C. H.: A nonlinear degenerate diffusion equation not in divergence form.Z. Angew. Math. Phys. 51 (2000), 149-159. Zbl 0961.35077, MR 1745296, 10.1007/PL00001503; reference:[17] Wiegner, M.: A degenerate diffusion equation with a nonlinear source term.Nonlinear Anal., Theory Methods Appl. 28 (1997), 1977-1995. Zbl 0874.35061, MR 1436366, 10.1016/S0362-546X(96)00027-2; reference:[18] Zimmer, T.: On a degenerate parabolic equation. IWR Heidelberg.Preprint 93-05 (1993).

الاتاحة: http://hdl.handle.net/10338.dmlcz/140598

المؤلفون: Sakthivel, Kumarasamy, Balachandran, Krishnan, Sowrirajan, Rangarajan, Kim, Jeong-Hoon

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وصف الملف: application/pdf

Relation: mr:MR2479312; zbl:Zbl 1177.93021; reference:[1] Adams R. A., Fournier J. F.: Sobolev Spaces.Second edition. Academic Press, New York 2003 Zbl 1098.46001, MR 2424078; reference:[2] Khodja F. Ammar, Benabdallah, A., Dupaix C.: Null controllability of some reaction diffusion systems with one control force.J. Math. Anal. Appl. 320 (2006), 928–943 MR 2226005; reference:[3] Amster P., Averbuj C. G., Mariani M. C.: Solutions to a stationary nonlinear Black–Scholes type equation.J. Math. Anal. Appl. 276 (2002), 231–238 Zbl 1027.60077, MR 1944348; reference:[4] Amster P., Averbuj C. G., Mariani M. C., Rial D.: A Black–Scholes option pricing model with transaction costs.J. Math. Anal. Appl. 303 (2005), 688–695 Zbl 1114.91044, MR 2122570; reference:[5] Anita S., Barbu V.: Null controllability of nonlinear convective heat equation.ESAIM: Control, Optimization and Calculus of Variations 5 (2000), 157–173 MR 1744610; reference:[6] Barbu V.: Controllability of parabolic and Navier–Stokes equations.Scientiae Mathematicae Japonicae 56 (2002), 143–211 Zbl 1010.93054, MR 1911840; reference:[7] Black F., Scholes M.: The pricing of options and corporate liabilities.J. Political Economics 81 (1973), 637–659 Zbl 1092.91524; reference:[8] Bouchouev I., Isakov V.: The inverse problem of option pricing.Inverse Problems 13 (1997), L11–L17 Zbl 0894.90014, MR 1474358; reference:[9] Bouchouev I., Isakov V.: Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets.Inverse problems 15 (1999), R95–R116 Zbl 0938.35190, MR 1696930; reference:[10] Chae D., Imanivilov, O. Yu., Kim M. S.: Exact controllability for semilinear parabolic equations with Neumann boundary conditions.J. Dynamical Control Systems 2 (1996), 449–483 MR 1420354; reference:[11] Doubova A., Fernandez-Cara E., Gonzalez-Burgos, M., Zuazua E.: On the controllability of parabolic systems with a nonlinear term involving the state and the gradient.SIAM J. Control Optim. 41 (2002), 789–819 Zbl 1038.93041, MR 1939871; reference:[12] Egger H., Engl H. W.: Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates.Inverse Problems 21 (2005) 1027–1045 Zbl 1205.65194, MR 2146819; reference:[13] Fursikov A. V., Imanuvilov O. Yu.: Controllability of Evolution Equations.Lecture Notes Series 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul 1996 Zbl 0862.49004, MR 1406566; reference:[14] Hörmander L.: Linear Partial Differential Operators I – IV.Springer–Verlag, Berlin 1985; reference:[15] Imanuvilov O. Yu.: Boundary controllability of parabolic equations.Sbornik Mathematics 187 (1995), 879–900 MR 1349016; reference:[16] Imanuvilov O. Yu., Yamamoto M.: Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations.Publ. Res. Inst. Math. Sci. 39 (2003), 227–274 Zbl 1065.35079, MR 1987865; reference:[17] Ingber L., Wilson J. K.: Statistical mechanics of financial markets: Exponential modifications to Black–Scholes.Mathematical and Computer Modelling 31 (2000) 167–192 Zbl 1042.91524, MR 1761486; reference:[18] Jódar L., Sevilla-Peris P., Cortes J. C., Sala R.: A new direct method for solving the Black–Scholes equations.Appl. Math. Lett. 18 (2005), 29–32 MR 2121550; reference:[19] Kangro R., Nicolaides R.: Far field boundary conditions for Black–Scholes equations.SIAM J. Numer. Anal. 38 (2000), 1357–1368 Zbl 0990.35013, MR 1790037; reference:[20] Sakthivel K., Balachandran, K., Sritharan S. S.: Controllability and observability theory of certain parabolic integro-differential equations.Comput. Math. Appl. 52 (2006), 1299–1316 MR 2307079; reference:[21] Sakthivel K., Balachandran, K., Lavanya R.: Exact controllability of partial integrodifferential equations with mixed boundary conditions.J. Math. Anal. Appl. 325 (2007), 1257–1279 Zbl 1191.93013, MR 2270082; reference:[22] Sowrirajan R., Balachandran K.: Determination of a source term in a partial differential equation arising in finance.Appl. Anal. (to appear) Zbl 1170.35328, MR 2536788; reference:[23] Widdicks M., Duck P. W., Andricopoulos A. D., Newton D. P.: The Black–Scholes equation revisited: Asymptotic expansions and singular perturbations.Mathematical Finance 15 (2005), 373–371 Zbl 1124.91342, MR 2132196; reference:[24] Wilmott I., Howison, S., Dewynne J.: The Mathematics of Financial Derivatives.Cambridge University Press, Cambridge 1995 Zbl 0842.90008, MR 1357666

الاتاحة: http://hdl.handle.net/10338.dmlcz/135882

المؤلفون: Jia, Shanghui, Li, Deli, Liu, Tang, Zhang, Shuhua

مصطلحات موضوعية: keyword:integro-differential equations, keyword:mixed finite element methods, keyword:mixed regularized Green’s functions, keyword:asymptotic expansions, keyword:interpolation defect correction, keyword:interpolation postprocessing, keyword:a posteriori error estimators, msc:45K05, msc:65M12, msc:65M60, msc:65R20, msc:76M10, msc:76S05

وصف الملف: application/pdf

Relation: mr:MR2382288; zbl:Zbl 1177.76408; reference:[1] I. Babuška: The finite element method with Lagrangian multipliers.Numer. Math. 20 (1973), 179–192. MR 0359352, 10.1007/BF01436561; reference:[2] H. Blum: Asymptotic Error Expansion and Defect in the Finite Element Method.University of Heidelberg, Institut für Angewandte Mathematik, Heidelberg, .; reference:[3] H. Blum, Q. Lin, R. Rannacher: Asymptotic error expansion and Richardson extrapolation for linear finite elements.Numer. Math. 49 (1986), 11–38. MR 0847015, 10.1007/BF01389427; reference:[4] F. Brezzi: On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers.RAIRO, Anal. Numér. 2 (1974), 129–151. Zbl 0338.90047, MR 0365287; reference:[5] H. Brunner, Y. Lin, S. Zhang: Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods.J. Integral Equations Appl. 10 (1998), 375–396. MR 1669667, 10.1216/jiea/1181074245; reference:[6] J. R. Cannon, Y. Lin: Non-classical $H^1$ projection and Galerkin methods for nonlinear parabolic integro-differential equations.Calcolo 25 (1988), 187–201. MR 1053754, 10.1007/BF02575943; reference:[7] J. R. Cannon Y. Lin: A priori $L^2$ error estimates for finite element methods for nonlinear diffusion equations with memory.SIAM J. Numer. Anal. 27 (1990), 595–607. MR 1041253, 10.1137/0727036; reference:[8] C. Chen, Y. Huang: Higher Accuracy Theory of FEM.Hunan Science Press, Changsha, 1995.; reference:[9] J. Douglas, Jr., J. E. Roberts: Global estimates for mixed methods for second order elliptic equations.Math. Comput. 44 (1985), 39–52. MR 0771029, 10.1090/S0025-5718-1985-0771029-9; reference:[10] R. E. Ewing, Y. Lin, T. Sun, J. Wang, S. Zhang: Sharp $L^2$ error estimates and superconvergence of mixed finite element methods for nonFickian flows in porous media.SIAM J. Numer. Anal. 40 (2002), 1538–1560. MR 1951906, 10.1137/S0036142900378406; reference:[11] R. E. Ewing, Y. Lin, J. Wang: A numerical approximation of nonFickian flows with mixing length growth in porous media.Acta Math. Univ. Comenian. (N. S.) 70 (2001), 75–84. MR 1865361; reference:[12] R. E. Ewing, Y. Lin, J. Wang: A backward Euler method for mixed finite element approximations of nonFickian flows with non-smooth data in porous media.Preprint.; reference:[13] R. E. Ewing, Y. Lin, J. Wang, S. Zhang: $L^{\infty }$-error estimates and superconvergence in maximum norm of mixed finite element methods for nonFickian flows in porous media.Int. J. Numer. Anal. Model. 2 (2005), 301–328. MR 2112650; reference:[14] G. Fairweather, Q. Lin, Y. Lin, J. Wang, S. Zhang: Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods.SIAM J. Numer. Anal. 44 (2006), 1122–1149. MR 2231858, 10.1137/040614293; reference:[15] P. Helfrich: Asymptotic expansion for the finite element approximations of parabolic problems.Bonn. Math. Schr. 158 (1984), 11–30. MR 0793413; reference:[16] S. Jia, D. Li, S. Zhang: Asymptotic expansions and Richardson extrapolation of approximate solutions for integro-differential equations by mixed finite element methods.Adv. Comput. Math (to appear). MR 2447252; reference:[17] M. N. LeRoux, V. Thomée: Numerical solutions of semilinear integro-differential equations of parabolic type with nonsmooth data.SIAM J. Numer. Anal. 26 (1989), 1291–1309. 10.1137/0726075; reference:[18] Q. Lin, I. H. Sloan, R. Xie: Extrapolation of the iterated-collocation method for integral equations of the second kind.SIAM J. Numer. Anal. 27 (1990), 1535–1541. MR 1080337, 10.1137/0727090; reference:[19] Q. Lin, N. Yan: The Construction and Analysis of High Efficiency Finite Element Methods.Hebei University Publishers, , 1996.; reference:[20] Q. Lin, S. Zhang: An immediate analysis for global superconvergence for integrodifferential equations.Appl. Math. 42 (1997), 1–21. MR 1426677, 10.1023/A:1022264125558; reference:[21] Q. Lin, S. Zhang, N. Yan: Asymptotic error expansion and defect correction for Sobolev and viscoelasticity type equations.J. Comput. Math. 16 (1998), 57–62. MR 1606093; reference:[22] Q. Lin, S. Zhang, N. Yan: High accuracy analysis for integrodifferential equations.Acta Math. Appl. Sin. 14 (1998), 202–211. MR 1620823, 10.1007/BF02677428; reference:[23] Q. Lin, S. Zhang, N. Yan: Methods for improving approximate accuracy for hyperbolic integro-differential equations.Syst. Sci. Math. Sci. 10 (1997), 282–288. MR 1469188; reference:[24] Q. Lin, S. Zhang, N. Yan: Extrapolation and defect correction for diffusion equations with boundary integral conditions.Acta Math. Sci. 17 (1997), 409–412. MR 1613231; reference:[25] Q. Lin, S. Zhang, N. Yan: An acceleration method for integral equations by using interpolation post-processing.Adv. Comput. Math. 9 (1998), 117–128. MR 1662762, 10.1023/A:1018925103993; reference:[26] T. Lin, Y. Lin, M. Rao, S. Zhang: Petrov-Galerkin methods for linear Volterra integro-differential equations.SIAM J. Numer. Anal. 38 (2000), 937–963. MR 1781210, 10.1137/S0036142999336145; reference:[27] Y. Lin: On maximum norm estimates for Ritz-Volterra projections and applications to some time-dependent problems.J. Comput. Math. 15 (1997), 159–178. MR 1448820; reference:[28] Y. Lin, V. Thomée, L. Wahlbin: Ritz-Volterra projection onto finite element spaces and applications to integrodifferential and related equations.SIAM J. Numer. Anal. 28 (1991), 1047–1070. MR 1111453, 10.1137/0728056; reference:[29] G. Marchuk, V. Shaidurov: Difference Methods and Their Extrapolation.Springer, New York, 1983. MR 0705477; reference:[30] B. Neta, J. Igwe: Finite difference versus finite elements for solving nonlinear integro-differential equations.J. Math. Anal. Appl. 112 (1985), 607–618. MR 0813623, 10.1016/0022-247X(85)90266-5; reference:[31] A. K. Pani, V. Thomée, L. Wahlbin: Numerical methods for hyperbolic and parabolic integro-differential equations.J. Integral Equations Appl. 4 (1992), 533–584. MR 1200801, 10.1216/jiea/1181075713; reference:[32] I. H. Sloan, V. Thomée: Time discretization of an integro-differential equation of parabolic type.SIAM J. Numer. Anal. 23 (1986), 1052–1061. MR 0859017, 10.1137/0723073; reference:[33] V. Thomée, N. Zhang: Error estimates for semidiscrete finite element methods for parabolic integro-differential equations.Math. Comput. 53 (1989), 121–139. MR 0969493, 10.2307/2008352; reference:[34] J. Wang: Superconvergence and extrapolation for mixed finite element methods on rectangular domains.Math. Comput. 56 (1991), 477–503. Zbl 0729.65084, MR 1068807, 10.1090/S0025-5718-1991-1068807-0; reference:[35] J. Wang: Asymptotic expansions and $L^{\infty }$-error estimates for mixed finite element methods for second order elliptic problems.Numer. Math. 55 (1989), 401–430. MR 0997230, 10.1007/BF01396046; reference:[36] N. Yan, K. Li: An extrapolation method for BEM.J. Comput. Math. 2 (1989), 217–224. Zbl 0673.65072, MR 1016842; reference:[37] S. Zhang, T. Lin, Y. Lin, M. Rao: Extrapolation and a-posteriori error estimators of Petrov-Galerkin methods for non-linear Volterra integro-differential equations.J. Comp. Math. 19 (2001), 407–422. MR 1842853; reference:[38] A. Zhou, C. B. Liem, T. M. Shih, T. Lü: A multi-parameter splitting extrapolation and a parallel algorithm.Syst. Sci. Math. Sci. 10 (1997), 253–260. MR 1469184; reference:[39] Q. Zhu, Q. Lin: Superconvergence Theory of the Finite Element Methods.Hunan Science Press, , 1989.

الاتاحة: http://hdl.handle.net/10338.dmlcz/134697

المؤلفون: Shaw, Simon, Whiteman, J. R.

مصطلحات موضوعية: msc:45D05, msc:45K05, msc:65M15, msc:73F15

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/700266

المؤلفون: Szomolay, Barbara

مصطلحات موضوعية: keyword:asymptotic behavior of solutions, keyword:hyperbolic PDE of degenerate type, msc:35B40, msc:35L20, msc:35L70, msc:35L80, msc:45K05, msc:74H45

وصف الملف: application/pdf

Relation: mr:MR2045846; zbl:Zbl 1098.35033; reference:[1] Aassila M.: Some remarks on a second order evolution equation.Electron. J. Diff. Equations, Vol. 1998 (1998), No. 18, pp.1-6. Zbl 0902.35073, MR 1629704; reference:[2] Aassila M.: Decay estimates for a quasilinear wave equation of Kirchhoff type.Adv. Math. Sci. Appl. 9 1 (1999), 371-381. Zbl 0939.35028, MR 1690380; reference:[3] Aassila M.: Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms.Comment. Math. Univ. Carolinae 40.2 (1999), 223-226. MR 1732643; reference:[4] Dix J.G., Torrejón R.M.: A quasilinear integrodifferential equation of hyperbolic type.Differential Integral Equations 6 (1993), 2 431-447. MR 1195392; reference:[5] Dix J.G.: Decay of solutions of a degenerate hyperbolic equation.Electron. J. Diff. Equations, Vol. 1998 (1998), No. 21, pp.1-10. Zbl 0911.35075, MR 1637075; reference:[6] Matsuyama T., Ikehata R.: Energy decay for the wave equations II: global existence and decay of solutions.J. Fac. Sci. Univ. Tokio, Sect. IA, Math. 38 (1991), 239-250.

الاتاحة: http://hdl.handle.net/10338.dmlcz/119368

المؤلفون: Fengler, Martin J., Michel, Dominik, Michel, Volker

مصطلحات موضوعية: msc:42C40, Spline-Wavelets, GRACE , GOCE , Sobolev-Raum, regular surface, Harmonische Spline-Funktion, msc:41A15, msc:86A22, ball, Mehrskalenanalyse, CHAMP , GRACE , GOCE , Kugelfunktion, reguläre Fläche, Regularisierung, Inverses Problem, ddc:510, msc:45K05, Kugel

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URL الوصول: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::14d018fb4d2993a70ea23e660b0a3e40
https://kluedo.ub.uni-kl.de/files/1623/SFG_16.pdf

المؤلفون: Prüss, Jan

مصطلحات موضوعية: keyword:maximal regularity, keyword:sectorial operators, keyword:interpolation, keyword:trace theorems, keyword:elliptic and parabolic initial-boundary value problems, keyword:dynamic boundary conditions, msc:34G10, msc:35G10, msc:35K20, msc:35K90, msc:45K05, msc:47D06

وصف الملف: application/pdf

Relation: mr:MR1981536; zbl:Zbl 1010.35064; reference:[1] G. Da Prato, P. Grisvard: Sommes d’opérateurs linéaires et équations différentielles opérationelles.J. Math. Pures Appl. 54 (1975), 305–387. MR 0442749; reference:[2] G. Dore, A. Venni: On the closedness of the sum of two closed operators.Math. Z. 196 (1987), 189–201. MR 0910825, 10.1007/BF01163654; reference:[3] J. Escher, J. Prüss, G. Simonett: Analytic solutions of the Stefan problem with Gibbs-Thomson correction.(to appear).; reference:[4] J. Escher, J. Prüss, G. Simonett: Analytic solutions of the free boundary value problem for the Navier-Stokes equation.(to appear).; reference:[5] P. Grisvard: Spaci di trace e applicazioni.Rend. Math. 5 (1972), 657–729. MR 0341059; reference:[6] M. Hieber, J. Prüss: Maximal Regularity of Parabolic Problems.Monograph in preparation, 2001.; reference:[7] N. Kalton, L. Weis: The $H^\infty $-calculus and sums of closed operators.Math. Ann (to appear). MR 1866491; reference:[8] H. Komatsu: Fractional powers of operators.Pacific J. Math. 1 (1966), 285–346. Zbl 0154.16104, MR 0201985; reference:[9] O. A. Ladyženskaya, V. A. Solonnikov, N. N. Ural’ceva: Linear and Quasilinear Equations of Parabolic Type, vol. 23.Transl. Math. Monographs. Amer. Math. Soc., 1968. MR 0241822; reference:[10] J. Prüss, H. Sohr: On operators with bounded imaginary powers in Banach spaces.Math. Z. 203 (1990), 429–452. MR 1038710, 10.1007/BF02570748; reference:[11] P. E. Sobolevskii: Fractional powers of coercively positive sums of operators.Soviet Math. Dokl. 16 (1975), 1638–1641. Zbl 0333.47010, MR 0482314

الاتاحة: http://hdl.handle.net/10338.dmlcz/134160

المؤلفون: Ntouyas, Sotiris K.

مصطلحات موضوعية: keyword:Leray-Schauder Alternative, keyword:a priori bounds, keyword:partial functional integrodifferential equations, keyword:global existence, msc:34K30, msc:35R10, msc:45K05, msc:47D06

وصف الملف: application/pdf

Relation: mr:MR1645312; zbl:Zbl 0910.35136; reference:[1] Bochenek, J.: Second order semilinear Volterra integrodifferential equation in Banach space,.Ann. Pol. Math. 57 (1992), 231–241. Zbl 0786.45013, MR 1201850; reference:[2] Dugundji, J., Granas, A.: Fixed Point Theory, Vol. I.Monographie Matematyczne, PNW Warsawa, 1982.; reference:[3] Friedman, A.: Partial differential equations.Holt, Rinehat and Winston,, New York, 1969. Zbl 0224.35002, MR 0445088; reference:[4] Frigon, M., Granas, A.: Resultats du type de Leray-Schauder pour des contractions multivoques.Topol. Methods Nonlinear Anal. 4 (1994), 197–208. MR 1321812; reference:[5] Lee, J., O’Regan, D.: Topological transversality. Applications to initial value problems.Ann. Pol. Math. 48 (1988), 247–252. MR 0978675; reference:[6] Lee, J., O’Regan, D.: Existence results for differential delay equations-I.J. Differential Equations 102 (1993), 342–359. MR 1216733; reference:[7] MacCamy, R.: An integro-differential equation with applications in heat flow.Quart. Appl. Math. 35 (1977/78), 1–19. MR 0452184; reference:[8] Ntouyas, S., Sficas, Y., Tsamatos, P.: Existence results for initial value problems for neutral functional differential equations.J. Differential Equations 114 (1994), 527–537. MR 1303038; reference:[9] Ntouyas, S., Tsamatos, P.: Initial and boundary value problems for functional integrodifferential equations.J. Appl. Math. Stoch. Analysis 10 (1997), 157–168. MR 1453468; reference:[10] Ntouyas, S., Tsamatos, P.: Global existence for functional integrodifferential equations of delay and neutral type.Applicable Analysis 54 (1994), 251–262. MR 1379636; reference:[11] Travis, C., Webb, G.: Cosine families and abstract nonlinear second order differential equations.Acta Math. Hungarica 32 (1978), 75–96. MR 0499581; reference:[12] Travis, C., Webb, G.: An abstract second order semilinear Volterra integrodifferential equation.SIAM J. Math. Anal. 10 (1979), 412–424. MR 0523855; reference:[13] Travis, C., Webb, G.: Existence and stability for partial functional differential equations.Trans. Amer. Math. Soc. 200 (1974), 395–418. MR 0382808; reference:[14] Webb, G.: An abstract semilinear Volterra integrodifferential equation.Proc. Amer. Math. Soc. 69 (1978), 255–260. Zbl 0388.45012, MR 0467214; reference:[15] Yorke, J.: A continuous differential equation in Hilbert space without existence.Funkcial. Ekvac. 13 (1970), 19–21. Zbl 0248.34061, MR 0264196

الاتاحة: http://hdl.handle.net/10338.dmlcz/107650

المؤلفون: Lin, Qun, Zhang, Shuhua

مصطلحات موضوعية: keyword:integrodifferential equations, keyword:global superconvergence, keyword:immediate analysis, keyword:postprocessing, keyword:finite element method, keyword:parabolic, keyword:hyperbolic, msc:45K05, msc:65B05, msc:65M60, msc:65N30, msc:65R20

وصف الملف: application/pdf

Relation: mr:MR1426677; zbl:Zbl 0902.65090; reference:[1] J. Cannon, Y. Lin: A Galerkin procedure for diffusion equations with boundary integral conditions.Int. J. Eng. Sci. 28 (1990), 579–587. MR 1059777, 10.1016/0020-7225(90)90087-Y; reference:[2] M. Křížek, P. Neittaanmäki: On Finite Element Approximation of Variational Problems and Applications.Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Essex, 1989. MR 1066462; reference:[3] Q. Lin: A new observation in FEM.Proc. Syst. Sci. & Syst. Eng., Great Wall (H.K.), Culture Publish Co., 1991, pp. 389–391.; reference:[4] Q. Lin, N. Yan, A. Zhou: A rectangle test for interpolated finite elements, ibid.217–229.; reference:[5] Q. Lin, Q. Zhu: The Preprocessing and Postprocessing for the Finite Element Method.Shanghai Scientific & Technical Publishers, 1994.; reference:[6] Y. Lin: Galerkin methods for nonlinear parabolic integrodifferential equations with nonlinear boundary conditions.SIAM J. Numer. Anal. 27 (1990), 608–621. Zbl 0703.65095, MR 1041254, 10.1137/0727037; reference:[7] Y. Lin, T. Zhang: The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type.Applications of Mathematics 36 (1991), no. 2, 123–133. MR 1097696; reference:[8] Y. Lin, V. Thomée, L. Wahlbin: Ritz-Volterra projection on finite element spaces and applications to integrodifferential and related equations.SIAM J. Numer. Anal. 28 (1991), 1047–1070. MR 1111453, 10.1137/0728056; reference:[9] V. Thomée: Galerkin Finite Element Methods for Parabolic Problems.Lect. Notes in Math., 1054, 1984. MR 0744045; reference:[10] V. Thomée, J. Xu, N. Zhang: Superconvergence of the gradient in piecewise linear finite element approximation to a parabolic problem.SIAM J. Numer. Anal. 26 (1989), 553–573. MR 0997656, 10.1137/0726033; reference:[11] V. Thomée, N. Zhang: Error estimates for semidiscrete finite element methods for parabolic integrodifferential equations.Math. Comp. 53 (1989), 121–139. MR 0969493, 10.2307/2008352; reference:[12] M. Wheeler: A priori $L_2$ error estimates for Galerkin approximations to parabolic partial differential equations.SIAM J. Numer. Anal. 10 (1973), 723–759. MR 0351124, 10.1137/0710062; reference:[13] Q. Zhu, Q. Lin: Superconvergence Theory of the Finite Element Methods.Hunan Science Press, 1990.

الاتاحة: http://hdl.handle.net/10338.dmlcz/134341

المؤلفون: Matejíčka, Ladislav

مصطلحات موضوعية: msc:45G10, msc:45K05, msc:45L05

وصف الملف: application/pdf

Relation: mr:MR1335844; zbl:Zbl 0832.45007; reference:[1] AMIEZ G., GREMAUD P. A.: On a numerical approach to Stefan-like problems.Numer. Math. 59 (1991), 71-89. Zbl 0731.65107, MR 1103754; reference:[2] BERGER A. E., BREZIS H., ROGERS J. C. W.: A numerical method for solving the problem $\partial_t u(t) - \Delta f(u(t)) = 0$.RAIRO Modél. Math. Anal. Numér. 13 (1979), 297-312. MR 0555381; reference:[3] GAJEWSKI H., GRÖGER K., ZACHARIAS K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademia-Verlag. Berlin, 1974. MR 0636412; reference:[4] CHEN C., THOMÉE V., WAHLBIN L. B.: Finite element approximation of a parabolic integrodifferential equation with a weakly singular kernel.Math. Comp. 58 (1992), 587-602. MR 1122059; reference:[5] JEROME J. W., ROSE M. E.: Error estimates for the multidimensional two-phase Stefan Problem.Math. Comp. 39 (1982), 377-414. Zbl 0505.65060, MR 0669635; reference:[6] JÄGER W., KAČÚR J.: Approximation of porous medium type systems by non degenerate elliptic systems.Preprint, Universität Heilderberg, SFB 123 (1990).; reference:[7] JÄGER W., KAČÚR J.: Solution of porous medium type systems by linear approximation schemes.Numer. Math. 60 (1991), 407-427. Zbl 0744.65060, MR 1137200; reference:[8] KAČÚR J.: Method of Rothe in Evolution Equations.BSB Teubner Verlag, Leipzig, 1985. Zbl 0582.65084, MR 0834176; reference:[9] KAČÚR J.: Application of Rothe's method to evolution integrodifferential equations.J. Reine Angew. Math. 388 (1988), 73-105. Zbl 0638.65098, MR 0944184; reference:[10] KAČÚR J.-HANDLOVIČOVÁ A.-KAČÚROVÁ M.: Solution of nonlinear diffusion problems by linear approximation schemes.Preprint, Comenius University, Bratislava (Accepted to SIAM J. Numer. Anal.). Zbl 0792.65070, MR 1249039; reference:[11] KAČÚROVÁ M.: Solution of porous medium type problems with nonlinear boundary conditions by linear approximation schemes.(To appear).; reference:[12] MacCAMY R. C.-WONG J. S. W.: Stability theorems for some functional equations.Trans. Amer. Math. Soc. 164 (1972), 1-37. Zbl 0274.45012, MR 0293355; reference:[13] MAGENES E.-NOCHETTO R. H.- VERDI C.: Energy error estimates for a linear scheme to approximate nonlinear parabolic equations.RAIRO Model. Math. Anal. Numer. 21 (1987), 655-678. MR 0921832; reference:[14] MAGENES E.-VERDI C.-VISINTIN A.: Theoretical and numerical results on the two-phase Stefan problem.SIAM J. Numer. Anal. 26 (1989), 1425-1438. Zbl 0738.65092, MR 1025097; reference:[15] McLEAN W.-THOMEE V.: Numerical solution of an evolution equation with a positive type memory term.J. Austral. Math. Soc. Ser. B (Submitted). Zbl 0791.65105, MR 1225703; reference:[16] SLODIČKA M.: Application of Rothe's method to evolution integrodifferential systems.Comment. Math. Univ. Carolin. 30 (1989), 57-70. Zbl 0674.65110, MR 0995701; reference:[17] SLODIČKA M.: On a numerical approach to nonlinear degenerate parabolic problems.Preprint, Comenius University, M6 (1992).; reference:[18] SLODIČKA M.: Numerical solution of a parabolic equation with a weakly singular positive-type memory term.Preprint, Comenius University, M7 (1992). MR 1447332

الاتاحة: http://hdl.handle.net/10338.dmlcz/136638

المؤلفون: Avgerinos, Evgenios P., Papageorgiou, Nikolaos S.

مصطلحات موضوعية: keyword:retract, keyword:absolute retract, keyword:path-connected, keyword:Vietoris continuous, keyword:$h$-continuous, keyword:orientor field, msc:34A60, msc:34K30, msc:45K05

وصف الملف: application/pdf

Relation: mr:MR1364483; zbl:Zbl 0836.34019; reference:[1] Avgerinos E.P.: On the existence of solutions for Volterra integrable inclusions in Banach spaces.Jour. Appl. Math. and Stoch. Anal. 6 (1993), 261-270. MR 1238603; reference:[2] Bressan A., Cellina A., Fryszkowski A.: A class of absolute retracts in spaces of integrable functions.Proc. Amer. Math. Soc. 112 (1991), 413-418. Zbl 0747.34014, MR 1045587; reference:[3] Cellina A.: On the set of solutions to Lipschitzian differential inclusions.Diff. and Integral Equations 1 (1988), 495-500. Zbl 0723.34009, MR 0945823; reference:[4] DeBlasi F.S., Myjak J.: On the solution set for differential inclusions.Bull. Pol. Acad. Sci. 33 (1985), 17-23.; reference:[5] DeBlasi F.S., Myjak J.: On continuous approximations for multifunctions.Pacific Journal of Math. 123 (1986), 9-31. MR 0834135; reference:[6] DeBlasi F.S., Pianigiani G., Staicu V.: On the Solution Sets of Some Nonconvex Hyperbolic Differential Inclusions.Università degli Studi di Roma, Prepr. 117, Oct. 1992.; reference:[7] Dugundji J.: Topology.Allyn and Bacon Inc., Boston, 1966. Zbl 0397.54003, MR 0193606; reference:[8] Gorniewicz L.: On the solution set of differential inclusions.JMAA 113 (1986), 235-247. MR 0826673; reference:[9] Hiai F., Umegaki H.: Integrals conditional expectations and martingales of multivalued functions.J. Multivariate Anal. 7 (1977), 149-182. Zbl 0368.60006, MR 0507504; reference:[10] Himmelberg C., Van Fleck F.: A note on the solution sets of differential inclusions.Rocky Mountain J. Math. 12 (1982), 621-625. MR 0683856; reference:[11] Klein E., Thompson A.: Theory of Correspondences.Wiley, New York, 1984. Zbl 0556.28012, MR 0752692; reference:[12] Kuratowski K.: Topology II.Academic Press, London, 1966. MR 0217751; reference:[13] Levin V.: Borel sections of many valued maps.Siberian Math. J. 19 (1979), 434-438. Zbl 0409.54048; reference:[14] Nadler S.B.: Multivalued contraction mappings.Pacific J. Math. 30 (1969), 475-483. MR 0254828; reference:[15] Pachpatte B.G.: A note on Gronwall-Bellman inequality.J. Math. A.A. 44 (1973), 758-762. Zbl 0274.45011, MR 0335721; reference:[16] Papageorgiou N.S.: Convergence theorems for Banach space valued integrable multifunctions.Intern. J. Math. Sci. 10 (1987), 433-442. Zbl 0619.28009, MR 0896595; reference:[17] Papageorgiou N.S.: On measurable multifunctions with applications to random multivalued equations.Math. Japonica 32 (1987), 437-464. Zbl 0634.28005, MR 0914749; reference:[18] Papageorgiou N.S.: Decomposable sets in the Lebesgue-Bochner spaces.Comment. Math. Univ. Sancti Pauli 37 (1988), 49-62. Zbl 0679.46032, MR 0942305; reference:[19] Papageorgiou N.S.: Existence of solutions for integrodifferential inclusions in Banach spaces.Comment. Math. Univ. Carolinae 32 (1991), 687-696. Zbl 0746.34035, MR 1159815; reference:[20] Ricceri B.: Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes.Atti. Acad. Naz. Linci. U. Sci. Fiz. Math. Nat. 81 (1987), 283-286. Zbl 0666.47030, MR 0999821; reference:[21] Rybinski L.: A fixed point approach in the study of the solution sets of Lipschitzian functional-differential inclusions.JMAA 160 (1991), 24-46. Zbl 0735.34016, MR 1124074; reference:[22] Staicu V.: On a non-convex hyperbolic differential inclusion.Proc. Edinb. Math. Soc., in press. Zbl 0769.34018; reference:[23] Tsukada M.: Convergence of best approximations in a smooth Banach space.Journal of Approx. Theory 40 (1984), 301-309. Zbl 0545.41042, MR 0740641; reference:[24] Wagner D.: Surveys of measurable selection theorems.SIAM J. Control. Optim. 15 (1977), 857-903. MR 0486391

الاتاحة: http://hdl.handle.net/10338.dmlcz/118771