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Title: Blow up above stationary solutions of certain nonlinear parabolic equations  (English)
Author: Fila, Marek
Author: Filo, Ján
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 29
Issue: 1
Year: 1988
Pages: 179-193
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Category: math
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Summary:
MSC: 35B30
MSC: 35B35
MSC: 35B40
MSC: 35K55
MSC: 35K65
idZBL: Zbl 0659.35059
idMR: MR937560
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Date available: 2008-06-05T21:32:09Z
Last updated: 2012-04-28
Stable URL: http://hdl.handle.net/10338.dmlcz/106608
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Reference: [1] D. G. ARONSON M. G. CRANDALL L. A. PELETIER: Stabilization of solutions of a degenerate nonlinear diffusion problem.Nonlinear Analysis 6 (1982), 1001-1022. MR 0678053
Reference: [2] J. M. BALL: Remarks on blow-up and nonexistence theorems for nonlinear evolution equation.Quart. J. Math. Oxford 28 (1977), 473-486. MR 0473484
Reference: [3] M. BERTCH R. ROSTAMIAN: The principle of linearized stability for a class of degenerate diffusion equations.J. Differential Equations 57 (1985), 373-405. MR 0790282
Reference: [4] H. BREZIS L. NIRENBERG: Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents.Commun. Pure Appl. Math. 36 (1983), 437-477. MR 0709644
Reference: [5] M. FILA, J. FILO: Stabilization of solutions of certain one-dimensional degenerate diffusion equations.Mathematica Slovaca 37 (1987), 217-229. Zbl 0619.35064, MR 0899439
Reference: [6] M. FILA J. FILO: A blow-up result for nonlinear diffusion equations.to appear in Mathematica Slovaca. MR 1016350
Reference: [7] M. FILA J. FILO: Global behaviour of solutions to some nonlinear diffusion equations.to appear. MR 1046291
Reference: [8] J. FILO: On solutions of perturbed fast diffusion equation.Aplikace Matematiky 32 (1987) . MR 0909544
Reference: [9] V. A. GALAKTIONOV: A boundary value problem for the nonlinear parabolic equation $u_t = {\Delta}u^{\alpha+1} + u{\beta}$.Differential Equations 17 (1981), 551-555 (Russian). MR 0616920
Reference: [10] B. KAWOHL: Rearrangements and Convexity of Level Sets in PDE.Springer-Velag, Berlin, 1985 . Zbl 0593.35002, MR 0810619
Reference: [11] M. LANGLAIS D. PHILLIPS: Stabilization of solutions of nonlinear and degenerate evolution equations.Nonlinear Analysis 9 (1985), 321-333. MR 0783581
Reference: [12] H. A. LEVINE P. E. SACKS: Some existence and nonexistence theorems for solutions of degenerate parabolic equations.J. Differential Equations 52 (1984), 135-161. MR 0741265
Reference: [13] P. L. LIONS: Asymptotic behavior of some nonlinear heat equations.Physica D 5 (1982), 293-306. MR 0680566
Reference: [14] H. MATANO: Existence of nontrivial unstable sets for equilibгiums of strongly order-preseving systems.J. Fac. Sc. Univ. Tokyo 30 (1984), 645-673. MR 0731522
Reference: [15] M. NAKAO: Existence, nonexistence and some asymptotic behavior of global solutions of a nonlinear degenerate parabolic equation.Math. Rep., College Gen. Ed. Kyushu Univ., 1983, 1-21 . MR 0737351
Reference: [16] M. NAKAO: $L^p$-estimates of solutions of some nonlinear degenerate diffusion equations.J. Math. Soc. Japan 37 (1985), 41-63. Zbl 0584.65073, MR 0769776
Reference: [17] W. M. NI P. E. SACKS J. TAVANTZIS: On the asymptotic behavior of solutions of certain quasilinear parabolic equations.J. Differential Equations 54 (1984), 97-120. MR 0756548
Reference: [18] L. E. PAYNE D. H. SATTINGER: Saddle points and instability of nonlinear hyperbolic equations.Israel J. Math. 22 (1975), 273-303. MR 0402291
Reference: [19] M. H. PROTTER H. F. WEINBERGER: Maximum Principles in Partial Differential Equations.Prentice Hall, Englewood Cliffs, 1967. MR 0219861
Reference: [20] P. E. SACKS: Global behavior for a class of nonlinear evolution equations.SIAM J. Math. Anal. 16 (1985). Zbl 0572.35062, MR 0777465
Reference: [21] N. STERNBERG: Blow up near higher modes of nonlinear wave equations.Trans. Amer. Math. Soc. 296 (1986), 315-325. MR 0837814
Reference: [22] M. TSUTSUMI: Existence and nonexistence of global solutions for nonlinear parabolic equations.Publ. R.I.M.S., Қyoto Univ. 8 (1972/73), 211-229. Zbl 0248.35074, MR 0312079
Reference: [23] F. WEISSLER: Local existence and nonexistence for semilinear parabolic equations in $L^p$.Indiana Univ. Math. J. 29 (1980), 79-102. MR 0554819
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