المؤلفون: Yang, Shanshan, Jiang, Hongbiao, Lin, Yinhe

مصطلحات موضوعية: keyword:compressible isentropic Navier-Stokes-Poisson equation, keyword:unipolar, keyword:energy solution, keyword:blow-up, msc:35B44, msc:35Q35

وصف الملف: application/pdf

Relation: mr:MR4339121; zbl:Zbl 07442484; reference:[1] Cho, Y., Jin, B. J.: Blow-up of viscous heat-conducting compressible flows.J. Math. Anal. Appl. 320 (2006), 819-826. Zbl 1121.35110, MR 2225997, 10.1016/j.jmaa.2005.08.005; reference:[2] Dong, J., Ju, Q.: Blow-up of smooth solutions to compressible quantum Navier-Stokes equations.Sci. Sin., Math. 50 (2020), 873-884 Chinese. 10.1360/N012018-00134; reference:[3] Dong, J., Zhu, J., Wang, Y.: Blow-up for the compressible isentropic Navier-Stokes-Poisson equations.Czech. Math. J. 70 (2020), 9-19. Zbl 07217119, MR 4078344, 10.21136/CMJ.2019.0156-18; reference:[4] Gamba, I. M., Gualdani, M. P., Zhang, P.: On the blowing up of solutions to quantum hydrodynamic models on bounded domains.Monatsh Math. 157 (2009), 37-54. Zbl 1173.35106, MR 2504777, 10.1007/s00605-009-0092-4; reference:[5] Guo, B., Wang, G.: Blow-up of the smooth solution to quantum hydrodynamic models in $\mathbb R^d$.J. Differ. Equations 261 (2016), 3815-3842. Zbl 1354.35123, MR 3532056, 10.1016/j.jde.2016.06.007; reference:[6] Guo, B., Wang, G.: Blow-up of solutions to quantum hydrodynamic models in half space.J. Math. Phys. 58 (2017), Article ID 031505, 11 pages. Zbl 1359.76348, MR 3626024, 10.1063/1.4978331; reference:[7] Jiu, Q., Wang, Y., Xin, Z.: Remarks on blow-up of smooth solutions to the compressible fluid with constant and degenerate viscosities.J. Differ. Equations 259 (2015), 2981-3003. Zbl 1319.35194, MR 3360663, 10.1016/j.jde.2015.04.007; reference:[8] Lai, N.-A.: Blow up of classical solutions to the isentropic compressible Navier-Stokes equations.Nonlinear Anal., Real World Appl. 25 (2015), 112-117. Zbl 1327.35299, MR 3351014, 10.1016/j.nonrwa.2015.03.005; reference:[9] Lei, Z., Du, Y., Zhang, Q.: Singularities of solutions to compressible Euler equations with vacuum.Math. Res. Lett. 20 (2013), 41-50. Zbl 1284.35329, MR 3126720, 10.4310/MRL.2013.v20.n1.a4; reference:[10] Rozanova, O.: Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations.J. Differ. Equations 245 (2008), 1762-1774. Zbl 1154.35070, MR 2433485, 10.1016/j.jde.2008.07.007; reference:[11] Wang, G., Guo, B., Fang, S.: Blow-up of the smooth solutions to the compressible Navier-Stokes equations.Math. Methods Appl. Sci. 40 (2017), 5262-5272. Zbl 1383.35034, MR 3689262, 10.1002/mma.4384; reference:[12] Xin, Z.: Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density.Commun. Pure Appl. Math. 51 (1998), 229-240. Zbl 0937.35134, MR 1488513, 10.1002/(SICI)1097-0312(199803)51:33.0.CO;2-C; reference:[13] Xin, Z., Yan, W.: On blowup of classical solutions to the compressible Navier-Stokes equations.Commun. Math. Phys. 321 (2013), 529-541. Zbl 1287.35059, MR 3063918, 10.1007/s00220-012-1610-0

الاتاحة: http://hdl.handle.net/10338.dmlcz/149248

المؤلفون: Li, Huanyuan

مصطلحات موضوعية: keyword:Navier-Stokes-Korteweg equations, keyword:capillary fluid, keyword:blow-up criterion, keyword:vacuum, keyword:strong solutions, msc:35D35, msc:35Q35, msc:76D45

وصف الملف: application/pdf

Relation: mr:MR4218601; zbl:07332688; reference:[1] Bosia, S., Pata, V., Robinson, J. C.: A weak-$L^p$ Prodi-Serrin type regularity criterion for the Navier-Stokes equations.J. Math. Fluid Mech. 16 (2014), 721-725. Zbl 1307.35186, MR 3267544, 10.1007/s00021-014-0182-5; reference:[2] Cho, Y., Kim, H.: Unique solvability for the density-dependent Navier-Stokes equations.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 59 (2004), 465-489. Zbl 1066.35070, MR 2094425, 10.1016/j.na.2004.07.020; reference:[3] Grafakos, L.: Classical Fourier Analysis.Graduate Texts in Mathematics 249, Springer, New York (2008). Zbl 1220.42001, MR 2445437, 10.1007/978-0-387-09432-8; reference:[4] Huang, X., Wang, Y.: Global strong solution to the 2D nonhomogeneous incompressible MHD system.J. Differ. Equations 254 (2013), 511-527. Zbl 1253.35121, MR 2990041, 10.1016/j.jde.2012.08.029; reference:[5] Huang, X., Wang, Y.: Global strong solution with vacuum to the two dimensional density-dependent Navier-Stokes system.SIAM J. Math. Anal. 46 (2014), 1771-1788. Zbl 1302.35294, MR 3200422, 10.1137/120894865; reference:[6] Huang, X., Wang, Y.: Global strong solution of 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity.J. Differ. Equations 259 (2015), 1606-1627. Zbl 1318.35064, MR 3345862, 10.1016/j.jde.2015.03.008; reference:[7] Kim, H.: A blow-up criterion for the nonhomogeneous incompressible Navier-Stokes equations.SIAM J. Math. Anal. 37 (2006), 1417-1434. Zbl 1141.35432, MR 2215270, 10.1137/S0036141004442197; reference:[8] Ladyzhenskaya, O. A., Solonnikov, V. A., Ural'tseva, N. N.: Linear and Quasilinear Equations of Parabolic Type.Translations of Mathematical Monographs 23, American Mathematical Society, Providence (1968). Zbl 0174.15403, MR 0241822, 10.1090/mmono/023; reference:[9] Li, H.: A blow-up criterion for the density-dependent Navier-Stokes-Korteweg equations in dimension two.Acta Appl. Math. 166 (2020), 73-83. Zbl 07181473, MR 4077229, 10.1007/s10440-019-00255-3; reference:[10] Sohr, H.: The Navier-Stokes Equations. An Elementary Functional Analytic Approach.Birkhäuser Advanced Texts, Birkhäuser, Basel (2001). Zbl 0983.35004, MR 3013225, 10.1007/978-3-0348-0551-3; reference:[11] Tan, Z., Wang, Y.: Strong solutions for the incompressible fluid models of Korteweg type.Acta Math. Sci., Ser. B, Engl. Ed. 30 (2010), 799-809. Zbl 1228.76038, MR 2675787, 10.1016/S0252-9602(10)60079-3; reference:[12] Wang, T.: Unique solvability for the density-dependent incompressible Navier-Stokes-Korteweg system.J. Math. Anal. Appl. 455 (2017), 606-618. Zbl 1373.35257, MR 3665121, 10.1016/j.jmaa.2017.05.074; reference:[13] Xu, X., Zhang, J.: A blow-up criterion for 3D compressible magnetohydrodynamic equations with vacuum.Math. Models Methods Appl. Sci. 22 (2012), Article ID 1150010, 23 pages. Zbl 1388.76452, MR 2887666, 10.1142/S0218202511500102

الاتاحة: http://hdl.handle.net/10338.dmlcz/148509

المؤلفون: Dong, Jianwei, Zhu, Junhui, Wang, Yanping

مصطلحات موضوعية: keyword:compressible isentropic Navier-Stokes-Poisson equations, keyword:unipolar, keyword:bipolar, keyword:smooth solution, keyword:blow-up, msc:35B44, msc:35Q35

وصف الملف: application/pdf

Relation: mr:MR4078344; zbl:07217119; reference:[1] Cai, H., Tan, Z.: Existence and stability of stationary solutions to the compressible Navier-Stokes-Poisson equations.Nonlinear Anal., Real World Appl. 32 (2016), 260-293. Zbl 1348.35183, MR 3514925, 10.1016/j.nonrwa.2016.04.010; reference:[2] Cai, H., Tan, Z.: Asymptotic stability of stationary solutions to the compressible bipolar Navier-Stokes-Poisson equations.Math. Methods Appl. Sci. 40 (2017), 4493-4513. Zbl 1373.35233, MR 3672880, 10.1002/mma.4320; reference:[3] Cho, Y., Jin, B.: Blow up of viscous heat-conducting compressible flows.J. Math. Anal. Appl. 320 (2006), 819-826. Zbl 1121.35110, MR 2225997, 10.1016/j.jmaa.2005.08.005; reference:[4] Du, D. P., Li, J. Y., Zhang, K. J.: Blow-up of smooth solutions to the Navier-Stokes equations for compressible isothermal fluids.Commun. Math. Sci. 11 (2013), 541-546. Zbl 1305.76089, MR 3002564, 10.4310/CMS.2013.v11.n2.a11; reference:[5] Hsiao, L., Li, H. L.: Compressible Navier-Stokes-Poisson equations.Acta Math. Sci., Ser. B 30 (2010), 1937-1948. Zbl 1240.35406, MR 2778703, 10.1016/S0252-9602(10)60184-1; reference:[6] Hsiao, L., Li, H. L., Yang, T., Zou, C.: Compressible non-isentropic bipolar Navier-Stokes-Poisson system in $\mathbb{R}^{3}$.Acta Math. Sci., Ser. B 31 (2011), 2169-2194. Zbl 1265.35265, MR 2931498, 10.1016/S0252-9602(11)60392-5; reference:[7] Jiang, F., Tan, Z.: Blow-up of viscous compressible reactive self-gravitating gas.Acta Math. Appl. Sin., Engl. Ser. 28 (2012), 401-408. Zbl 1359.35131, MR 2914383, 10.1007/s10255-012-0152-8; reference:[8] Jiu, Q. S., Wang, Y. X., Xin, Z. P.: Remarks on blow-up of smooth solutions to the compressible fluid with constant and degenerate viscosities.J. Differ. Equations 259 (2015), 2981-3003. Zbl 1319.35194, MR 3360663, 10.1016/j.jde.2015.04.007; reference:[9] Lai, N. A.: Blow up of classical solutions to the isentropic compressible Navier-Stokes equations.Nonlinear Anal., Real World Appl. 25 (2015), 112-117. Zbl 1327.35299, MR 3351014, 10.1016/j.nonrwa.2015.03.005; reference:[10] Rozanova, O.: Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations.J. Differ. Equations 245 (2008), 1762-1774. Zbl 1154.35070, MR 2433485, 10.1016/j.jde.2008.07.007; reference:[11] Tan, Z., Wang, Y. J.: Blow-up of smooth solutions to the Navier-Stokes equations of compressible viscous heat-conducting fluids.J. Aust. Math. Soc. 88 (2010), 239-246. Zbl 1191.35210, MR 2629933, 10.1017/S144678871000008X; reference:[12] Tang, T., Zhang, Z. J.: Blow-up of smooth solution to the compressible Navier-Stokes-Poisson equations.Bull. Malays. Math. Sci. Soc. 39 (2016), 1487-1497. Zbl 1358.35133, MR 3549976, 10.1007/s40840-015-0256-4; reference:[13] Wang, G. W., Guo, B. L.: Blow-up of the smooth solutions to the compressible Navier-Stokes equations.Math. Methods Appl. Sci. 40 (2017), 5262-5272. Zbl 1383.35034, MR 3689262, 10.1002/mma.4384; reference:[14] Wang, Y. Z., Wang, K. Y.: Asymptotic behavior of classical solutions to the compressible Navier-Stokes-Poisson equations in three and higher dimensions.J. Differ. Equations 259 (2015), 25-47. Zbl 1317.35211, MR 3335919, 10.1016/j.jde.2015.01.042; reference:[15] Xie, H. Z.: Blow-up of smooth solutions to the Navier-Stokes-Poisson equations.Math. Methods Appl. Sci. 34 (2011), 242-248. Zbl 1206.35201, MR 2779329, 10.1002/mma.1353; reference:[16] Xin, Z. P.: Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density.Commun. Pure Appl. Math. 51 (1998), 229-240. Zbl 0937.35134, MR 1488513, 10.1002/(SICI)1097-0312(199803)51:3\229::AID-CPA1\3.0.CO;2-C; reference:[17] Xin, Z. P., Yan, W.: On blowup of classical solutions to the compressible Navier-Stokes equations.Commun. Math. Phys. 321 (2013), 529-541. Zbl 1287.35059, MR 3063918, 10.1007/s00220-012-1610-0; reference:[18] Zhao, Z. Y., Li, Y. P.: Global existence and optimal decay rate of the compressible bipolar Navier-Stokes-Poisson equations with external force.Nonlinear Anal., Real World Appl. 16 (2014), 146-162. Zbl 1297.35195, MR 3123807, 10.1016/j.nonrwa.2013.09.014; reference:[19] Zou, C.: Asymptotical behavior of bipolar non-isentropic compressible Navier-Stokes-Poisson system.Acta Math. Appl. Sin., Engl. Ser. 32 (2016), 813-832. Zbl 1364.35291, MR 3552850, 10.1007/s10255-016-0596-3

الاتاحة: http://hdl.handle.net/10338.dmlcz/148040

المؤلفون: Ling, Amy Poh Ai, Shimojō, Masahiko

مصطلحات موضوعية: keyword:quasilinear heat equation, keyword:total blow-up, keyword:blow-up only at space infinity, msc:35B44, msc:35K59

وصف الملف: application/pdf

Relation: mr:MR3985858; zbl:Zbl 07088852; reference:[1] Galaktionov, V. A.: Asymptotic behavior of unbounded solutions of the nonlinear equation $u_t=(u^\sigma u_x)_x+u^\beta$ near a ``singular'' point.Sov. Math., Dokl. 33 (1986), 840-844 translated from Dokl. Akad. Nauk SSSR 288 1986 1293-1297. Zbl 0629.35061, MR 0852454; reference:[2] Galaktionov, V. A., Kurdyumov, S. P., Mikhailov, A. P., Samarskii, A. A.: Unbounded solutions of the Cauchy problem for the parabolic equation $u_t=\nabla (u^{\sigma }\nabla u)+u^{\beta}$.Sov. Phys., Dokl. 25 (1980), 458-459 translated from Dokl. Akad. Nauk SSSR 252 1980 1362-1364. Zbl 515.35045, MR 0581597; reference:[3] Giga, Y., Umeda, N.: Blow-up directions at space infinity for solutions of semilinear heat equations.Bol. Soc. Parana. Mat. (3) 23 (2005), 9-28 correction ibid. 24 2006 19-24. Zbl 1173.35531, MR 2242285, 10.5269/bspm.v23i1-2.7450; reference:[4] Giga, Y., Umeda, N.: On blow-up at space infinity for semilinear heat equations.J. Math. Anal. Appl. 316 (2006), 538-555. Zbl 1106.35029, MR 2206688, 10.1016/j.jmaa.2005.05.007; reference:[5] Lacey, A. A.: The form of blow-up for nonlinear parabolic equations.Proc. R. Soc. Edinb., Sect. A 98 (1984), 183-202. Zbl 0556.35077, MR 0765494, 10.1017/S0308210500025609; reference:[6] Ladyženskaja, O. A., Solonnikov, V. A., Ural'ceva, N. N.: Linear and Quasilinear Equations of Parabolic Type.Translations of Mathematical Monographs 23. AMS, Providence (1968). Zbl 0174.15403, MR 0241822, 10.1090/mmono/023; reference:[7] Mochizuki, K., Suzuki, R.: Blow-up sets and asymptotic behavior of interfaces for quasilinear degenerate parabolic equations in $R^N$.J. Math. Soc. Japan 44 (1992), 485-504. Zbl 0805.35065, MR 1167379, 10.2969/jmsj/04430485; reference:[8] Oleinik, O. A., Kalašinkov, A. S., Chou, Y.-L.: The Cauchy problem and boundary problems for equations of the type of non-stationary filtration.Izv. Akad. Nauk SSSR, Ser. Mat. 22 (1958), 667-704 Russian. Zbl 0093.10302, MR 0099834; reference:[9] Samarskii, A. A., Galaktionov, V. A., Kurdyumov, S. P., Mikhailov, A. P.: Blow-up in Quasilinear Parabolic Equations.De Gruyter Expositions in Mathematics 19. Walter de Gruyter, Berlin (1995). Zbl 1020.35001, MR 1330922, 10.1515/9783110889864.535; reference:[10] Seki, Y.: On directional blow-up for quasilinear parabolic equations with fast diffusion.J. Math. Anal. Appl. 338 (2008), 572-587. Zbl 1144.35030, MR 2386440, 10.1016/j.jmaa.2007.05.033; reference:[11] Seki, Y., Umeda, N., Suzuki, R.: Blow-up directions for quasilinear parabolic equations.Proc. R. Soc. Edinb., Sect. A, Math. 138 (2008), 379-405. Zbl 1167.35393, MR 2406697, 10.1017/S0308210506000801; reference:[12] Shimojō, M.: The global profile of blow-up at space infinity in semilinear heat equations.J. Math. Kyoto Univ. 48 (2008), 339-361. Zbl 1184.35078, MR 2436740, 10.1215/kjm/1250271415; reference:[13] Suzuki, R.: On blow-up sets and asymptotic behavior of interfaces of one-dimensional quasilinear degenerate parabolic equations.Publ. Res. Inst. Math. Sci. 27 (1991), 375-398. Zbl 0789.35024, MR 1121244, 10.2977/prims/1195169661

الاتاحة: http://hdl.handle.net/10338.dmlcz/147775

المؤلفون: Anada, Koichi, Ishiwata, Tetsuya, Ushijima, Takeo

مصطلحات موضوعية: keyword:Blow-up rate, type II blow-up, numerical estimate, scale invariance, rescaling algorithm, curvature flow, msc:35B44, msc:35K59, msc:65M99

وصف الملف: application/pdf

Relation: reference:[1] Anada, K., Fukuda, I., Tsutsumi, M.: Regional blow-up and decay of solutions to the Initial-Boundary value problem for $u_t = uu_{xx} − \gamma(u_x)^2 + ku^2$., Funkcialaj Ekvacioj, 39 (1996), pp. 363–387. MR 1433906; reference:[2] Anada, K., Ishiwata, T.: Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation., J. Differential Equations, 262 (2017), pp. 181–271. MR 3567485, 10.1016/j.jde.2016.09.023; reference:[3] Anada, K., Ishiwata, T., Ushijima, T.: A numerical method of estimating blow-up rates for nonlinear evolution equations by using rescaling algorithm., to appear in Japan J. Ind. Appl. Math. MR 3768236; reference:[5] Andrews, B.: Singularities in crystalline curvature flows., Asian J. Math., 6 (2002), pp. 101–122. MR 1902649, 10.4310/AJM.2002.v6.n1.a6; reference:[6] Angenent, S. B.: On the formation of singularities in the curve shortening flow., J. Diff. Geo. 33 (1991), pp. 601–633. MR 1100205, 10.4310/jdg/1214446558; reference:[7] Angenent, S. B., Velázquez, J. J. L.: Asymptotic shape of cusp singularities in curve shortening., Duke Math. J., 77 (1995), pp. 71–110. MR 1317628, 10.1215/S0012-7094-95-07704-7; reference:[8] Berger, M., Kohn, R. V.: A rescaling algorithm for the numerical calculation of blowing-up solutions., Cmmm. Pure Appl. Math., 41 (1988), pp. 841–863. MR 0948774, 10.1002/cpa.3160410606; reference:[9] Friedman, A., McLeod, B.: Blow-up of solutions of nonlinear degenerate parabolic equations., Arch. Rational Mech. Anal., 96 (1987), pp. 55–80. MR 0853975, 10.1007/BF00251413; reference:[10] Ishiwata, T., Yazaki, S.: On the blow-up rate for fast blow-up solutions arising in an anisotropic crystalline motion., J. Comput. Appl. Math., 159 (2003), pp. 55–64. MR 2022315, 10.1016/S0377-0427(03)00556-9; reference:[11] Watterson, P. A.: Force-free magnetic evolution in the reversed-field pinch., Thesis, Cambridge University (1985).; reference:[12] Winkler, M.: Blow-up in a degenerate parabolic equation., Indiana Univ. Math. J., 53 (2004), pp. 1415–1442. MR 2104284, 10.1512/iumj.2004.53.2451

الاتاحة: http://hdl.handle.net/10338.dmlcz/703052

المؤلفون: Ming, Sen, Yang, Han, Chen, Zili, Yong, Ls

مصطلحات موضوعية: keyword:liquid crystals system, keyword:critical Besov space, keyword:negative index, keyword:well-posedness, keyword:blow-up, msc:35B44, msc:35Q35, msc:76A15

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/146039

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

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

المؤلفون: Escudero, Carlos, Gazzola, Filippo, Hakl, Robert, Peral, Ireneo, Torres, Pedro José

مصطلحات موضوعية: keyword:higher order parabolic equation, keyword:existence of solution, keyword:blow-up in finite time, keyword:higher order elliptic equation, keyword:variational method, keyword:strongly singular boundary value problem, msc:34B16, msc:35G20, msc:35J50, msc:35J60, msc:35K25, msc:35K91

وصف الملف: application/pdf

Relation: mr:MR3432540; zbl:Zbl 06537671; reference:[1] Escudero, C., Gazzola, F., Peral, I.: Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian.J. Math. Pures Appl. (9) 103 (2015), 924-957. MR 3318175; reference:[2] Escudero, C., Hakl, R., Peral, I., Torres, P. J.: Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth.Math. Methods Appl. Sci. 37 (2014), 793-807. MR 3188526, 10.1002/mma.2836; reference:[3] Escudero, C., Hakl, R., Peral, I., Torres, P. J.: On radial stationary solutions to a model of non-equilibrium growth.Eur. J. Appl. Math. 24 (2013), 437-453. Zbl 1266.91051, MR 3053654, 10.1017/S0956792512000484; reference:[4] Escudero, C., Peral, I.: Some fourth order nonlinear elliptic problems related to epitaxial growth.J. Differ. Equations 254 (2013), 2515-2531. Zbl 1284.35435, MR 3016212, 10.1016/j.jde.2012.12.012

الاتاحة: http://hdl.handle.net/10338.dmlcz/144457

المؤلفون: Földes, Juraj

مصطلحات موضوعية: keyword:a priori estimates, keyword:Liouville theorems, keyword:blow-up rate, keyword:positive solution, keyword:indefinite parabolic problem, msc:35B09, msc:35B44, msc:35B45, msc:35B53, msc:35J61, msc:35K59

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/141526

المؤلفون: Chen, Jianqing

مصطلحات موضوعية: keyword:interpolation inequality, keyword:inhomogeneous nonlinear Schrödinger equation, keyword:harmonic potential, keyword:blow-up, keyword:global existence, keyword:standing waves, keyword:strong instability, msc:35J20, msc:35Q55

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الاتاحة: http://hdl.handle.net/10338.dmlcz/140601

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: Jiang, Lingyu, Wang, Yidong

مصطلحات موضوعية: keyword:compressible Navier-Stokes equations, keyword:classical solutions, keyword:blow up criterion, msc:35B44, msc:35Q30, msc:35Q35, msc:76D03

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/140562

المؤلفون: Neustupa, Jiří

مصطلحات موضوعية: keyword:Navier-Stokes equations, keyword:blow-up, keyword:weak solution, msc:35D40, msc:35Q30, msc:76D05

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/141317

المؤلفون: Perthame, Benoît

مصطلحات موضوعية: keyword:chemotaxis, keyword:angiogenesis, keyword:degenerate parabolic equations, keyword:kinetic equations, keyword:global weak solutions, keyword:blow-up, msc:35B40, msc:35B60, msc:35Q80, msc:92C17, msc:92C50

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/134584

المؤلفون: Quittner, Pavol

مصطلحات موضوعية: keyword:a priori estimate, keyword:blow-up rate, keyword:periodic solution, keyword:multiplicity, msc:35B45, msc:35J65, msc:35K20, msc:35K55, msc:35K60

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/134174

المؤلفون: Boni, Théodore K.

مصطلحات موضوعية: keyword:blow-up, keyword:global existence, keyword:asymptotic behavior, keyword:maximum principle, msc:35B40, msc:35K55, msc:35K60

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/119102

المؤلفون: Quittner, Pavol

مصطلحات موضوعية: keyword:Blow-up, keyword:global existence, keyword:apriori estimates, msc:35B40, msc:35K50, msc:35K60

وصف الملف: application/pdf

Relation: mr:MR1629705; zbl:Zbl 0911.35062; reference:[1] H. Brézis, R. E. L. Turner: On a class of superlinear elliptic problems.Comm. Partial Differ. Equations, 2 (1977), 601–614 MR 0509489; reference:[2] M. Fila: Boundedness of global solutions of nonlinear diffusion equations.J. Differ. Equations, 98 (1992), 226–240 Zbl 0764.35010, MR 1170469; reference:[3] M. Fila, H. Levine: On the boundedness of global solutions of abstract semi-linear parabolic equations.J. Math. Anal. Appl., 216 (1997), 654–666 MR 1489604; reference:[4] Y. Giga: A bound for global solutions of semilinear heat equations.Comm. Math. Phys., 103 (1986), 415–421 Zbl 0595.35057, MR 0832917; reference:[5] V. Galaktionov, J. L. Vázquez: Continuation of blow-up solutions of nonlinear heat equations in several space dimensions.Comm. Pure Applied Math., 50 (1997), 1–67 MR 1423231; reference:[6] T. Gu, M. Wang: Existence of positive stationary solutions and threshold results for a reaction-diffusion system.J. Diff. Equations, 130, (1996), 277–291 Zbl 0858.35059, MR 1410888; reference:[7] P. Quittner: Global solutions in parabolic blow-up problems with perturbations.Proc. 3rd European Conf. on Elliptic and Parabolic Problems, Pont-à-Mousson 1997, (to appear) MR 1628115; reference:[8] P. Quittner: Signed solutions for a semilinear elliptic problem.Differential and Integral Equations, (to appear) Zbl 1131.35339, MR 1666269

الاتاحة: http://hdl.handle.net/10338.dmlcz/107645

المؤلفون: Chen, Guowang, Wang, Shubin

مصطلحات موضوعية: keyword:nonlinear hyperbolic equation, keyword:initial boundary value problem, keyword:classical \linebreak global solution, keyword:blow up of solutions, msc:35L35, msc:35L75, msc:35Q72, msc:74H45, msc:74K10

وصف الملف: application/pdf

Relation: mr:MR1364488; zbl:Zbl 0839.35085; reference:[1] Zhuang Wei, Yang Guitong: Propagation of solitary waves in the nonlinear rods.Applied Mathematics and Mechanics 7 (1986), 571-581.; reference:[2] Zhang Shangyuan, Zhuang Wei: Strain solitary waves in the nonlinear elastic rods (in Chinese).Acta Mechanica Sinica 20 (1988), 58-66.; reference:[3] Chen Guowang, Yang Zhijian, Zhao Zhancai: Initial value problems and first boundary problems for a class of quasilinear wave equations.Acta Mathematicae Applicate Sinica 9 (1993), 289-301. Zbl 0822.35094, MR 1259814; reference:[4] Levine H.A.: Some additional remarks on the nonexistence of global solutions to nonlinear wave equations.SIAM J. Math. Anal. 5 (1974), 138-146. Zbl 0243.35069, MR 0399682; reference:[5] Levine H.A.: Instability & nonexistence of global solutions to nonlinear wave equations of the form $Pu_{tt}=-Au+F(u)$.Trans. of AMS 192 (1974), 1-21. MR 0344697

الاتاحة: http://hdl.handle.net/10338.dmlcz/118776

المؤلفون: Stará, Jana, John, Oldřich

مصطلحات موضوعية: keyword:parabolic systems, keyword:regularity of weak solutions, keyword:blow up, msc:35B65, msc:35D10, msc:35K40, msc:35K50, msc:35K55

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/118779

المؤلفون: Quittner, Pavol

مصطلحات موضوعية: keyword:global existence, keyword:blow up, keyword:semilinear parabolic equation, keyword:stationary solution, msc:35B30, msc:35B40, msc:35J65, msc:35K60

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/118561