Blow up above stationary solutions of certain nonlinear parabolic equations

 Access to full text

 Full (PDF)

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. (1982) MR0678053
2. J. M. BALL, Remarks on blow-up and nonexistence theorems for nonlinear evolution equation, Quart. J. Math. Oxford 28 (1977), 473-486. (1977) MR0473484
3. M. BERTCH R. ROSTAMIAN, The principle of linearized stability for a class of degenerate diffusion equations, J. Differential Equations 57 (1985), 373-405. (1985) MR0790282
4. H. BREZIS L. NIRENBERG, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Commun. Pure Appl. Math. 36 (1983), 437-477. (1983) MR0709644
5. M. FILA, J. FILO, Stabilization of solutions of certain one-dimensional degenerate diffusion equations, Mathematica Slovaca 37 (1987), 217-229. (1987) Zbl0619.35064MR0899439
6. M. FILA J. FILO, A blow-up result for nonlinear diffusion equations, to appear in Mathematica Slovaca. MR1016350
7. M. FILA J. FILO, Global behaviour of solutions to some nonlinear diffusion equations, to appear. MR1046291
8. J. FILO, On solutions of perturbed fast diffusion equation, Aplikace Matematiky 32 (1987) . (1987) MR0909544
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). (1981) MR0616920
10. B. KAWOHL, Rearrangements and Convexity of Level Sets in PDE, Springer-Velag, Berlin, 1985 . (1985) Zbl0593.35002MR0810619
11. M. LANGLAIS D. PHILLIPS, Stabilization of solutions of nonlinear and degenerate evolution equations, Nonlinear Analysis 9 (1985), 321-333. (1985) MR0783581
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. (1984) MR0741265
13. P. L. LIONS, Asymptotic behavior of some nonlinear heat equations, Physica D 5 (1982), 293-306. (1982) MR0680566
14. H. MATANO, Existence of nontrivial unstable sets for equilibгiums of strongly order-preseving systems, J. Fac. Sc. Univ. Tokyo 30 (1984), 645-673. (1984) MR0731522
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 . (1983) MR0737351
16. M. NAKAO, $L^p$-estimates of solutions of some nonlinear degenerate diffusion equations, J. Math. Soc. Japan 37 (1985), 41-63. (1985) Zbl0584.65073MR0769776
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. (1984) MR0756548
18. L. E. PAYNE D. H. SATTINGER, Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273-303. (1975) MR0402291
19. M. H. PROTTER H. F. WEINBERGER, Maximum Principles in Partial Differential Equations, Prentice Hall, Englewood Cliffs, 1967. (1967) MR0219861
20. P. E. SACKS, Global behavior for a class of nonlinear evolution equations, SIAM J. Math. Anal. 16 (1985). (1985) Zbl0572.35062MR0777465
21. N. STERNBERG, Blow up near higher modes of nonlinear wave equations, Trans. Amer. Math. Soc. 296 (1986), 315-325. (1986) MR0837814
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. (1972) Zbl0248.35074MR0312079
23. F. WEISSLER, Local existence and nonexistence for semilinear parabolic equations in $L^p$, Indiana Univ. Math. J. 29 (1980), 79-102. (1980) MR0554819