| 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 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35B30 |
| MSC:
|
35B35 |
| MSC:
|
35B40 |
| MSC:
|
35K55 |
| MSC:
|
35K65 |
| idZBL:
|
Zbl 0659.35059 |
| idMR:
|
MR937560 |
| . |
| Date available:
|
2008-06-05T21:32:09Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106608 |
| . |
| Reference:
|
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| 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:
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[13] P. L. LIONS: Asymptotic behavior of some nonlinear heat equations.Physica D 5 (1982), 293-306. MR 0680566 |
| Reference:
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[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 |
| . |
