المؤلفون: Nam, Bui Duc, Nhan, Nguyen Huu, Ngoc, Le Thi Phuong, Long, Nguyen Thanh

مصطلحات موضوعية: keyword:system of nonlinear wave equations of Kirchhoff-Carrier type, keyword:Balakrishnan-Taylor term, keyword:Faedo-Galerkin method, keyword:local existence, keyword:exponential decay, msc:35L20, msc:35L70, msc:35Q74, msc:37B25

وصف الملف: application/pdf

Relation: mr:MR4407355; zbl:Zbl 07547253; reference:[1] Balakrishnan, A. V., Taylor, L. W.: Distributed parameter nonlinear damping models for flight structures.Proceedings Damping 89. Report Number: WRDC-TR-89-3116 Volume II p. FDC-1 Flight Dynamics Laboratory, Chicago (1989), 9 pages.; reference:[2] Bass, R. W., Zes, D.: Spillover, nonlinearity and flexible structures.4th NASA Workshop on Computational Control of Flexible Aerospace Systems NASA Conference Publication 10065. NASA. Langley Research Center, Hampton (1991), 1-14.; reference:[3] Boulaaras, S.: Polynomial decay rate for a new class of viscoelastic Kirchhoff equation related with Balakrishnan-Taylor dissipationand logarithmic source terms.Alexandria Eng. J. 59 (2020), 1059-1071. 10.1016/j.aej.2019.12.013; reference:[4] Boulaaras, S., Draifia, A., Zennir, K.: General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping and logarithmic nonlinearity.Math. Methods Appl. Sci. 42 (2019), 4795-4814. 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G.: General decay rate estimates for viscoelastic wave equation with Balakrishnan-Taylor damping.Z. Angew. Math. Phys. 67 (2016), Article ID 32, 17 pages. Zbl 1353.35064, MR 3483881, 10.1007/s00033-016-0625-3; reference:[14] Ha, T. G.: Stabilization for the wave equation with variable coefficients and Balakrishnan-Taylor damping.Taiwanese J. Math. 21 (2017), 807-817. Zbl 1394.35044, MR 3684388, 10.11650/tjm/7828; reference:[15] Ha, T. G.: On the viscoelastic equation with Balakrishnan-Taylor damping and acoustic boundary conditions.Evol. Equ. Control Theory 7 (2018), 281-291. Zbl 1415.35042, MR 3810197, 10.3934/eect.2018014; reference:[16] Hao, J., Hou, Y.: Stabilization for wave equation of variable coefficients with Balakrishnan-Taylor damping and source term.Comput. Math. Appl. 76 (2018), 2235-2245. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/150331

المؤلفون: Zhang, Peixin, Zhu, Mingxuan

مصطلحات موضوعية: keyword:non-resistive magneto-micropolar fluid, keyword:local existence, msc:35A01, msc:35Q30, msc:76B03, msc:76W05

وصف الملف: application/pdf

Relation: mr:MR4396684; zbl:Zbl 07511501; reference:[1] Ahmadi, G., Shahinpoor, M.: Universal stability of magneto-micropolar fluid motions.Int. J. Engin. Sci. 12 (1974), 657-663. Zbl 0284.76009, MR 0443550, 10.1016/0020-7225(74)90042-1; reference:[2] Blömker, D., Nolde, C., Robinson, J. C.: Rigorous numerical verification of uniqueness and smoothness in a surface growth model.J. Math. Anal. Appl. 429 (2015), 311-325. Zbl 1315.65092, MR 3339076, 10.1016/j.jmaa.2015.04.025; reference:[3] Chemin, J.-Y., McCormick, D. S., Robinson, J. C., Rodrigo, J. L.: Local existence for the non-resistive MHD equations in Besov spaces.Adv. Math. 286 (2016), 1-31. Zbl 1333.35183, MR 3415680, 10.1016/j.aim.2015.09.004; reference:[4] Chen, M.: Global well-posedness of the 2D incompressible micropolar fluid flows with partial viscosity and angular viscosity.Acta Math. Sci., Ser. B, Engl. Ed. 33 (2013), 929-935. Zbl 1299.35043, MR 3072129, 10.1016/S0252-9602(13)60051-X; reference:[5] Chen, M., Xu, X., Zhang, J.: The zero limits of angular and micro-rotational viscosities for the two-dimensional micropolar fluid equations with boundary effect.Z. Angew. Math. Phys. 65 (2014), 687-710. Zbl 1300.35091, MR 3238510, 10.1007/s00033-013-0345-x; reference:[6] Cowin, S. C.: Polar fluids.Phys. Fluids 11 (1968), 1919-1927. Zbl 0179.56002, 10.1063/1.1692219; reference:[7] Erdoğan, M. E.: Polar effects in the apparent viscosity of suspension.Rheol. Acta 9 (1970), 434-438. 10.1007/BF01975413; reference:[8] Fefferman, C. L., McCormick, D. S., Robinson, J. C., Rodrigo, J. L.: Higher order commutator estimates and local existence for the non-resistive MHD equations and related models.J. Funct. Anal. 267 (2014), 1035-1056. Zbl 1296.35142, MR 3217057, 10.1016/j.jfa.2014.03.021; reference:[9] Fefferman, C. L., McCormick, D. S., Robinson, J. C., Rodrigo, J. L.: Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces.Arch. Ration. Mech. Anal. 223 (2017), 677-691. Zbl 1359.35150, MR 3590662, 10.1007/s00205-016-1042-7; reference:[10] Jiu, Q., Niu, D.: Mathematical results related to a two-dimensional magneto-hydrody-namic equations.Acta Math. Sci., Ser. B, Engl. Ed. 26 (2006), 744-756. Zbl 1188.35148, MR 2265204, 10.1016/S0252-9602(06)60101-X; reference:[11] Kato, T., Ponce, G.: Commutator estimates and the Euler and Navier-Stokes equations.Commun. Pure Appl. Math. 41 (1988), 891-907. Zbl 0671.35066, MR 0951744, 10.1002/cpa.3160410704; reference:[12] Kenig, C. E., Ponce, G., Vega, L.: Well-posedness of the initial value problem for the Korteweg-de Vries equation.J. Am. Math. Soc. 4 (1991), 323-347. Zbl 0737.35102, MR 1086966, 10.1090/S0894-0347-1991-1086966-0; reference:[13] {Ł}ukaszewicz, G.: Micropolar Fluids: Theory and Applications.Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston (1999). Zbl 0923.76003, MR 1711268, 10.1007/978-1-4612-0641-5; reference:[14] Ortega-Torres, E. E., Rojas-Medar, M. A.: Magneto-micropolar fluid motion: Global existence of strong solutions.Abstr. Appl. Anal. 4 (1999), 109-125. Zbl 0976.35055, MR 1810322, 10.1155/S1085337599000287; reference:[15] Rojas-Medar, M. A.: Magneto-micropolar fluid motion: Existence and uniqueness of strong solution.Math. Nachr. 188 (1997), 301-319. Zbl 0893.76006, MR 1484679, 10.1002/mana.19971880116; reference:[16] Rojas-Medar, M. A.: Magneto-micropolar fluid motion: On the convergence rate of the spectral Galerkin approximations.Z. Angew. Math. Mech. 77 (1997), 723-732. Zbl 0894.76093, MR 1479160, 10.1002/zamm.19970771003; reference:[17] Rojas-Medar, M. A., Boldrini, J. L.: Magneto-micropolar fluid motion: Existence of weak solutions.Rev. Mat. Complut. 11 (1998), 443-460. Zbl 0918.35114, MR 1666509, 10.5209/rev_REMA.1998.v11.n2.17276; reference:[18] Yuan, J.: Existence theorem and blow-up criterion of strong solutions to the magneto-micropolar fluid equations.Math. Methods Appl. Sci. 31 (2008), 1113-1130. Zbl 1137.76071, MR 2419091, 10.1002/mma.967; reference:[19] Yuan, B., Li, X.: Regularity of weak solutions to the 3D magneto-micropolar equations in Besov spaces.Acta Appl. Math. 163 (2019), 207-223. Zbl 1428.35409, MR 4008703, 10.1007/s10440-018-0220-z; reference:[20] Zhang, Z.: A regularity criterion for the three-dimensional micropolar fluid system in homogeneous Besov spaces.Electron. J. Qual. Theory Differ. Equ. 2016 (2016), Article ID 104, 6 pages. Zbl 1399.35307, MR 3578430, 10.14232/ejqtde.2016.1.104

الاتاحة: http://hdl.handle.net/10338.dmlcz/149566

المؤلفون: Ngoc, Le Thi Phuong, Long, Nguyen Thanh

مصطلحات موضوعية: keyword:nonlinear Love equation, keyword:Faedo-Galerkin method, keyword:local existence, keyword:blow up, keyword:exponential decay, msc:35L20, msc:35L70, msc:35Q74, msc:37B25

وصف الملف: application/pdf

Relation: mr:MR3470772; zbl:Zbl 06562152; reference:[1] Albert, J.: On the decay of solutions of the generalized Benjamin-Bona-Mahony equation.J. Math. Anal. Appl. 141 (1989), 527-537. Zbl 0697.35116, MR 1009061, 10.1016/0022-247X(89)90195-9; reference:[2] Amick, C. J., Bona, J. L., Schonbek, M. E.: Decay of solutions of some nonlinear wave equations.J. Differ. Equations 81 (1989), 1-49. Zbl 0689.35081, MR 1012198, 10.1016/0022-0396(89)90176-9; reference:[3] Benaissa, A., Messaoudi, S. A.: Exponential decay of solutions of a nonlinearly damped wave equation.NoDEA, Nonlinear Differ. Equ. Appl. 12 (2005), 391-399. Zbl 1102.35071, MR 2199380, 10.1007/s00030-005-0008-5; reference:[4] Chattopadhyay, A., Gupta, S., Singh, A. K., Sahu, S. A.: Propagation of shear waves in an irregular magnetoelastic monoclinic layer sandwiched between two isotropic half-spaces.International Journal of Engineering, Science and Technology 1 (2009), 228-244. MR 2380170; reference:[5] Clarkson, P. A.: New similarity reductions and Painlevé analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations.J. Phys. A, Math. Gen. 22 (1989), 3821-3848. Zbl 0711.35113, MR 1015235, 10.1088/0305-4470/22/18/020; reference:[6] Dutta, S.: On the propagation of Love type waves in an infinite cylinder with rigidity and density varying linearly with the radial distance.Pure Appl. Geophys. 98 (1972), 35-39. 10.1007/BF00875578; reference:[7] Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites nonlinéaires.Dunod; Gauthier-Villars, Paris (1969), French. MR 0259693; reference:[8] Long, N. T., Ngoc, L. T. P.: On a nonlinear wave equation with boundary conditions of two-point type.J. Math. Anal. Appl. 385 (2012), 1070-1093. Zbl 1228.35151, MR 2834912, 10.1016/j.jmaa.2011.07.034; reference:[9] Makhankov, V. G.: Dynamics of classical solitons (in non-integrable systems).Phys. Rep. 35 (1978), 1-128. MR 0481361, 10.1016/0370-1573(78)90074-1; reference:[10] Messaoudi, S. A.: Blow up and global existence in a nonlinear viscoelastic wave equation.Math. Nachr. 260 (2003), 58-66. Zbl 1035.35082, MR 2017703, 10.1002/mana.200310104; reference:[11] Nakao, M., Ono, K.: Global existence to the Cauchy problem of the semilinear wave equation with a nonlinear dissipation.Funkc. Ekvacioj, Ser. Int. 38 (1995), 417-431. Zbl 0855.35081, MR 1374429; reference:[12] Ngoc, L. T. P., Duy, N. T., Long, N. T.: A linear recursive scheme associated with the Love equation.Acta Math. Vietnam. 38 (2013), 551-562. Zbl 1310.35174, MR 3129917, 10.1007/s40306-013-0034-z; reference:[13] Ngoc, L. T. P., Duy, N. T., Long, N. T.: Existence and properties of solutions of a boundary problem for a Love's equation.Bull. Malays. Math. Sci. Soc. (2) 37 (2014), 997-1016. Zbl 1304.35231, MR 3295564; reference:[14] Ngoc, L. T. P., Duy, N. T., Long, N. T.: On a high-order iterative scheme for a nonlinear Love equation.Appl. Math., Praha 60 (2015), 285-298. Zbl 1363.65180, MR 3419963, 10.1007/s10492-015-0096-4; reference:[15] Ngoc, L. T. P., Long, N. T.: Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions.Commun. Pure Appl. Anal. 12 (2013), 2001-2029. Zbl 1267.35119, MR 3015668, 10.3934/cpaa.2013.12.2001; reference:[16] Ogino, T., Takeda, S.: Computer simulation and analysis for the spherical and cylindrical ion-acoustic solitons.J. Phys. Soc. Japan 41 (1976), 257-264. 10.1143/JPSJ.41.257; reference:[17] Paul, M. K.: On propagation of Love-type waves on a spherical model with rigidity and density both varying exponentially with the radial distance.Pure Appl. Geophys. 59 (1964), 33-37. Zbl 0135.23902, 10.1007/BF00880505; reference:[18] Radochová, V.: Remark to the comparison of solution properties of Love's equation with those of wave equation.Apl. Mat. 23 (1978), 199-207. MR 0492985; reference:[19] Seyler, C. E., Fenstermacher, D. L.: A symmetric regularized-long-wave equation.Phys. Fluids 27 (1984), 4-7. Zbl 0544.76170, 10.1063/1.864487; reference:[20] Truong, L. X., Ngoc, L. T. P., Dinh, A. P. N., Long, N. T.: Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74 (2011), 6933-6949. Zbl 1227.35075, MR 2833683, 10.1016/j.na.2011.07.015

الاتاحة: http://hdl.handle.net/10338.dmlcz/144843

المؤلفون: Shimotsuma, Daisuke, Yokota, Tomomi, Yoshii, Kentarou

مصطلحات موضوعية: keyword:local existence, keyword:complex Ginzburg-Landau equation, msc:35A01, msc:35Q55, msc:35Q56

وصف الملف: application/pdf

Relation: mr:MR3238845; zbl:Zbl 06362264; reference:[1] Clément, P., Okazawa, N., Sobajima, M., Yokota, T.: A simple approach to the Cauchy problem for complex Ginzburg-Landau equations by compactness methods.J. Differ. Equations 253 (2012), 1250-1263. Zbl 1248.35203, MR 2925912, 10.1016/j.jde.2012.05.002; reference:[2] Giga, M., Giga, Y., Saal, J.: Nonlinear Partial Differential Equations. Asymptotic Behavior of Solutions and Self-Similar Solutions.Progress in Nonlinear Differential Equations and Their Applications 79 Birkhäuser, Boston (2010). Zbl 1215.35001, MR 2656972; reference:[3] Ginibre, J., Velo, G.: The Cauchy problem in local spaces for the complex Ginzburg-Landau equation I. Compactness methods.Physica D 95 (1996), 191-228. Zbl 0889.35045, MR 1406282, 10.1016/0167-2789(96)00055-3; reference:[4] Ginibre, J., Velo, G.: The Cauchy problem in local spaces for the complex Ginzburg-Landau equation II. Contraction methods.Commun. Math. Phys. 187 (1997), 45-79. Zbl 0889.35046, MR 1463822, 10.1007/s002200050129; reference:[5] Kobayashi, Y., Matsumoto, T., Tanaka, N.: Semigroups of locally Lipschitz operators associated with semilinear evolution equations.J. Math. Anal. Appl. 330 (2007), 1042-1067. Zbl 1123.34044, MR 2308426, 10.1016/j.jmaa.2006.08.028; reference:[6] Levermore, C. D., Oliver, M.: The complex Ginzburg-Landau equation as a model problem.Dynamical Systems and Probabilistic Methods in Partial Differential Equations P. Deift et al. Lect. Appl. Math. 31 AMS, Providence 141-190 (1996). Zbl 0845.35003, MR 1363028; reference:[7] Matsumoto, T., Tanaka, N.: Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type.Nonlinear Anal. 69 (2008), 4025-4054. Zbl 1169.47045, MR 2463352, 10.1016/j.na.2007.10.035; reference:[8] Matsumoto, T., Tanaka, N.: Well-posedness for the complex Ginzburg-Landau equations.Current Advances in Nonlinear Analysis and Related Topics T. Aiki et al. GAKUTO Internat. Ser. Math. Sci. Appl. 32 Gakk$\bar o$tosho, Tokyo (2010), 429-442. Zbl 1208.35143, MR 2668292; reference:[9] Okazawa, N.: Smoothing effect and strong $L^2$-wellposedness in the complex Ginzburg-Landau equation.Differential Equations. Inverse and Direct Problems A. Favini, A. Lorenzi Lecture Notes in Pure and Applied Mathematics 251 CRC Press, Boca Raton (2006), 265-288. Zbl 1110.35030, MR 2275982, 10.1201/9781420011135.ch14; reference:[10] Okazawa, N., Yokota, T.: Monotonicity method applied to the complex Ginzburg-Landau and related equations.J. Math. Anal. Appl. 267 (2002), 247-263. Zbl 0995.35029, MR 1886827, 10.1006/jmaa.2001.7770; reference:[11] Okazawa, N., Yokota, T.: Perturbation theory for $m$-accretive operators and generalized complex Ginzburg-Landau equations.J. Math. Soc. Japan 54 (2002), 1-19. Zbl 1045.35080, MR 1864925, 10.2969/jmsj/1191593952; reference:[12] Okazawa, N., Yokota, T.: Non-contraction semigroups generated by the complex Ginz-burg-Landau equation.Nonlinear Partial Differential Equations and Their Applications N. Kenmochi et al. GAKUTO Internat. Ser. Math. Sci. Appl. 20 Gakk$\bar o$tosho, Tokyo (2004), 490-504. MR 2087493; reference:[13] Okazawa, N., Yokota, T.: Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation.Discrete Contin. Dyn. Syst. 28 (2010), 311-341. Zbl 1198.47089, MR 2629484, 10.3934/dcds.2010.28.311; reference:[14] Yang, Y.: On the Ginzburg-Landau wave equation.Bull. Lond. Math. Soc. 22 (1990), 167-170. Zbl 0663.35095, MR 1045289, 10.1112/blms/22.2.167; reference:[15] Yokota, T., Okazawa, N.: Smoothing effect for the complex Ginzburg-Landau equation (general case).Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13B (2006), suppl., 305-316. MR 2268800

الاتاحة: http://hdl.handle.net/10338.dmlcz/143860

المؤلفون: Rohde, C., Zajączkowski, W.

مصطلحات موضوعية: keyword:magnetohydrodynamics, keyword:radiation transport, keyword:local existence, msc:35L60, msc:35Q35, msc:76N10, msc:76W05

وصف الملف: application/pdf

Relation: mr:MR1994377; zbl:Zbl 1099.35060; reference:[1] H. Cabannes: Theoretical Magnetofluiddynamics.Academic Press, New York-London, 1970.; reference:[2] A. Dedner, C. Rohde: A scalar model problem in radiation hydrodynamics.In preparation.; reference:[3] K. O. Friedrichs: On the laws of relativistic electromagnetofluid dynamics.Comm. Pure Appl. Math. 27 (1974), 749–808. MR 0375928; reference:[4] K. O. Friedrichs: Conservation equations and the laws of motion in classical physics.Comm. Pure Appl. Math. 32 (1978), 123–131. Zbl 0379.35002, MR 0509916; reference:[5] K. Hamer: Nonlinear effects on the propagation of sound waves in a radiating gas.Quart. J. Mech. Appl. Math. 24 (1971), .; reference:[6] K. Ito: BV-solutions of the hyperbolic-elliptic system for a radiating gas.Preprint (1999).; reference:[7] T. Kato: The Cauchy problem for quasi-linear symmetric hyperbolic systems.Arch. Rational Mech. Anal. 58 (1975), 181–205. Zbl 0343.35056, MR 0390516, 10.1007/BF00280740; reference:[8] S. Kawashima, Y. Nikkuni and S. Nishibata: The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics.In: Analysis of systems of conservation laws, H. Freistühler (ed.), Chapman&Hall monographs and surveys in pure and applied mathematics 99, 1998, pp. 87–127. MR 1679939; reference:[9] A. Majda: Compressible Fluid Flow and Systems of Conservations Laws in Several Space Variables.Springer, 1984. MR 0748308; reference:[10] D. Mihalas: Radiation hydrodynamics.In: Computational methods for astrophysical fluid flow. Saas-Fee advanced course 27. Lecture notes 1997, O. Steiner et al. (eds.), Swiss Society for Astrophysics and Astronomy, 1998, pp. 161–261. Zbl 0940.76083; reference:[11] W. G. Vincenti, C. H. Krueger: Introduction to Physical Gas Dynamics.Wiley, 1965.; reference:[12] W. Zajączkowski: Non-characteristic mixed problems for nonlinear symmetric hyperbolic systems.Math. Methods Appl. Sci. 11 (1989), 139–168. 10.1002/mma.1670110201

الاتاحة: http://hdl.handle.net/10338.dmlcz/134532

المؤلفون: Ducomet, B.

مصطلحات موضوعية: keyword:compressible-Navier-Stokes-Schrödinger, keyword:time-dependent-Hartree-Fock approximation, keyword:local existence, keyword:global existence, msc:35Q35, msc:74D10, msc:76D05, msc:76N15, msc:76Y05, msc:81V35, msc:82D15

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Relation: mr:MR1844272; zbl:Zbl 1050.76063; reference:[1] P. Bonche, S. Koonin, J. W. Negele: One-dimensional nuclear dynamics in the TDHF approximation.Phys. Rev. C 13 (1976), 1226–1258. 10.1103/PhysRevC.13.1226; reference:[2] N. L. Balazs, B. Schürmann, K. Dietrich, L. P. Csernai: Scaling properties in the hydrodynamical description of heavy-ion reactions.Nucl. Phys. A424 (1984), 605–626. 10.1016/0375-9474(84)90012-5; reference:[3] J. Dechargé, D. Gogny: Hartree-Fock-Bogolyubov calculations with the D1 effective interaction on spherical nuclei.Phys. Rev. C 21 (1980), 1568–1593. 10.1103/PhysRevC.21.1568; reference:[4] B. Ducomet: Global existence for a simplified model of nuclear fluid in one dimension.J. Math. Fluid Mech. 2 (2000), 1–15. Zbl 0974.76013, MR 1755864, 10.1007/s000210050017; reference:[5] B. Ducomet, W. M. Zajaczkowski: On simplified models of nuclear fluids. In preparation.; reference:[6] A. L. Fetter, J. D. Walecka: Quantum Theory of Many-Particle Systems.McGraw-Hill, 1971.; reference:[7] K. Kuttler, D. Hicks: Weak solutions of initial-boundary value problems for class of nonlinear viscoelastic equations.Appl. Anal. 26 (1987), 33–43. MR 0916897, 10.1080/00036818708839699; reference:[8] P. Ring, P. Schuck: The Nuclear Many-Body Problem.Springer Verlag, 1980. MR 0611683; reference:[9] E. Sureau: La matière nucléaire.Hermann, 1998.; reference:[10] G. Ströhmer, W. M. Zajaczkowski: On the existence and properties of the rotationally symmetric equilibrium states of compressible barotropic self-gravitating fluids.Indiana Math. Journal 46 (1997), 1181–1220. MR 1631576; reference:[11] G. Ströhmer, W. M. Zajaczkowski: Local existence of solutions of free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids.Preprint (1998). MR 1683284; reference:[12] G. Ströhmer, W. M. Zajaczkowski: On stability of certain equilibrium solution for compressible barotropic viscous self-gravitating fluid motions bounded by a free surface.Preprint (1998).; reference:[13] C. Y. Wong, J. A. Maruhn, T. A. Welton: Dynamics of nuclear fluids. I. Foundations.Nucl. Phys. A253 (1975), 469–489.

الاتاحة: http://hdl.handle.net/10338.dmlcz/134011

المؤلفون: Człapiński, Tomasz

مصطلحات موضوعية: keyword:partial differential-functional equations, keyword:mixed problem, keyword:generalized solutions, keyword:local existence, keyword:bicharacteristics, keyword:successive approximations, msc:35A30, msc:35D05, msc:35L60, msc:35R10

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Relation: mr:MR1746704; zbl:Zbl 1010.35021; reference:[1] V. E. Abolina, A. D. Myshkis: Mixed problem for a semilinear hyperbolic system on a plane.Mat. Sb. 50 (1960), 423–442 (Russian).; reference:[2] P. Bassanini: On a boundary value problem for a class of quasilinear hyperbolic systems in two independent variables.Atti Sem. Mat. Fis. Univ. Modena 24 (1975), 343–372. MR 0430543; reference:[3] P. Bassanini: On a recent proof concerning a boundary value problem for quasilinear hyperbolic systems in the Schauder canonic form.Boll. Un. Mat. Ital. (5) 14-A (1977), 325–332. Zbl 0355.35059, MR 0492913; reference:[4] P. Bassanini: Iterative methods for quasilinear hyperbolic systems.Boll. Un. Mat. Ital. (6) 1-B (1982), 225–250. Zbl 0488.35056, MR 0654933; reference:[5] P. Bassanini, J. Turo: Generalized solutions of free boundary problems for hyperbolic systems of functional partial differential equations.Ann. Mat. Pura Appl. 156 (1990), 211–230. MR 1080217, 10.1007/BF01766980; reference:[6] P. Brandi, R. Ceppitelli: Generalized solutions for nonlinear hyperbolic systems in hereditary setting, preprint.; reference:[7] P. Brandi, Z. Kamont, A. Salvadori: Existence of weak solutions for partial differential-functional equations.(to appear).; reference:[8] L. Cesari: A boundary value problem for quasilinear hyperbolic systems in the Schauder canonic form.Ann. Sc. Norm. Sup. Pisa (4) 1 (1974), 311–358. MR 0380132; reference:[9] L. Cesari: A boundary value problem for quasilinear hyperbolic systems.Riv. Mat. Univ. Parma 3 (1974), 107–131. MR 0435616; reference:[10] S. Cinquini: Nuove ricerche sui sistemi di equazioni non lineari a derivate parziali in più variabili indipendenti.Rend. Sem. Mat. Fis. Univ. Milano 52 (1982).; reference:[11] M. Cinquini-Cibrario: Teoremi di esistenza per sistemi di equazioni non lineari a derivate parziali in più variabili indipendenti.Rend. Ist. Lombardo 104 (1970), 759–829. Zbl 0215.16202, MR 0296485; reference:[12] M. Cinquini-Cibrario: Sopra una classe di sistemi di equazioni non lineari a derivate parziali in più variabili indipendenti.Ann. Mat. Pura. Appl. 140 (1985), 223–253. MR 1553456, 10.1007/BF01776851; reference:[13] T. Człapiński: On the Cauchy problem for quasilinear hyperbolic systems of partial differential-functional equations of the first order.Zeit. Anal. Anwend. 10 (1991), 169–182. 10.4171/ZAA/439; reference:[14] T. Dzłapiński: On the mixed problem for quasilinear partial differential-functional equations of the first order.Zeit. Anal. Anwend. 16 (1997), 463–478. 10.4171/ZAA/773; reference:[15] T. Człapiński: Existence of generalized solutions for hyperbolic partial differential-functional equations with delay at derivatives.(to appear).; reference:[16] Z. Kamont, K. Topolski: Mixed problems for quasilinear hyperbolic differential-functional systems.Math. Balk. 6 (1992), 313–324. MR 1203465; reference:[17] A. D. Myshkis; A. M. Filimonov: Continuous solutions of quasilinear hyperbolic systems in two independent variables.Diff. Urav. 17 (1981), 488–500. (Russian) Zbl 1152.35071, MR 0610510; reference:[18] A. D. Myshkis, A. M. Filimonov: Continuous solutions of quasilinear hyperbolic systems in two independent variables.Proc. of Sec. Conf. Diff. Equat. and Appl., Rousse (1982), 524–529. (Russian); reference:[19] J. Turo: On some class of quasilinear hyperbolic systems of partial differential-functional equations of the first order.Czechoslovak Math. J. 36 (1986), 185–197. Zbl 0612.35082, MR 0831307; reference:[20] J. Turo: Local generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in two independent variables.Ann. Polon. Math. 49 (1989), 259–278. Zbl 0685.35065, MR 0997519, 10.4064/ap-49-3-259-278

الاتاحة: http://hdl.handle.net/10338.dmlcz/127528