@article{AIHPC_1999__16_3_335_0, author = {Souplet, Philippe and Weissler, Fred B.}, title = {Poincar\'e's inequality and global solutions of a nonlinear parabolic equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {16}, year = {1999}, pages = {335-371}, mrnumber = {1687278}, zbl = {0924.35065}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1999__16_3_335_0} }
Souplet, Philippe; Weissler, Fred B. Poincaré's inequality and global solutions of a nonlinear parabolic equation. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) pp. 335-371. http://gdmltest.u-ga.fr/item/AIHPC_1999__16_3_335_0/
[Ad] Sobolev Spaces, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030
,[AE] On the blow up of solutions for a convective reaction diffusion equation, Proc. Roy. Soc. Edinburgh., Vol. 123, 1993, pp. 433-460. | MR 1226611 | Zbl 0801.35038
and ,[Am] Existence and regularity for semilinear parabolic evolution equations, Ann. Scuola Norm. Sup. Pisa, Vol. 11, 4, 1984, pp. 593-676. | Numdam | MR 808425 | Zbl 0625.35045
,[AW] blow-up in IRN for a parabolic equation with a damping nonlinear gradient term, Progress in nonlinear differential equations 1992, N. G. Lloyd et al. Eds, Birkhäuser. | MR 1167826 | Zbl 0795.35051
and ,[BC]
and , to appear.[B] On the spectral theory of elliptic operators, I, Math. Ann., Vol. 142, 1961, pp. 22-30. | MR 209909 | Zbl 0104.07502
,[CW] Some blow up results for a nonlinear parabolic problem with a gradient term, SIAM J. Math. Anal., Vol. 20, 4, 1989, pp. 886-907. | MR 1000727 | Zbl 0682.35010
and ,[E]
, Personal communication.[F] Remarks on blow up for a nonlinear parabolic equation with a gradient term, Proc. Amer. Math. Soc., Vol. 111, 2, 1991, pp. 795-801. | MR 1052569 | Zbl 0768.35047
,[Fr1] Partial Differential Equations, 1969, Holt, Rinehart and Winston, Inc., New York. | MR 445088 | Zbl 0224.35002
,[Fr2] Blow up of solutions of parabolic equations, Nonlinear diffusion equations and their equilibrium states, I 1988, W. M. Ni et al. Eds, Springer. | MR 956073 | Zbl 0669.35047
,[H] Some bounds for principal frequency, Applicable Analysis, Vol. 7, 1978, pp. 247-254. | MR 492339 | Zbl 0383.35053
,[KP] Observations on blow up and dead cores for nonlinear parabolic equations, Math. Z., Vol. 202, 1989, pp. 207-217. | MR 1013085 | Zbl 0661.35053
and ,[LSU] Linear and Quasilinear Equations of Parabolic Type, 1968, Translations of Mathematical Monographs, Amer. Math. Soc., Providence, RI. | MR 241822 | Zbl 0174.15403
, and ,[LN] existence, large time behaviour and life span of solutions of a semilinear parabolic Cauchy problem, Trans. Amer. Math. Soc., Vol. 333, 1, 1992, pp. 365-378. | MR 1057781 | Zbl 0785.35011
and[LPSS] Analysis of convective reaction-diffusion equation (II), SIAM J. Math. Anal., Vol. 20, 1, 1989, pp. 133-147. | MR 977493 | Zbl 0702.35126
, , and ,[L] On the lowest eigenvalue of the Laplacian for the intersection of two domains, Invent. Math., Vol. 74, 1983, pp. 441-448. | MR 724014 | Zbl 0538.35058
,[Q1] Blow-up for semilinear parabolic equations with a gradient term, Math. Meth. Appl. Sc., Vol. 14, 1991, pp. 413-417. | MR 1119238 | Zbl 0768.35049
,[Q2] On global existence and stationary solutions for two classes of semilinear parabolic equations, Comment. Math. Univ. Carolinae, Vol. 34, 1, 1993, pp. 105-124. | MR 1240209 | Zbl 0794.35089
,[O] A note on Hayman's theorem on the bass note of a drum, Comment. Math. Helvetici, Vol. 52, 1 1977, pp. 545-555. | MR 459099 | Zbl 0374.52008
,[S1] Résultats d'explosion en temps fini pour une équation de la chaleur non linéaire, C. R. Acad. Sc. Paris, Vol. 321, Série I, 1995, pp. 721-726. | MR 1354713 | Zbl 0843.35044
,[S2] Finite time blow up for a nonlinear parabolic equation with a gradient term and applications, Math. Meth. Appl. Sc., Vol. 19, 1996, pp. 1317-1333. | MR 1412998 | Zbl 0858.35067
,[S3] Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations, Communications in Partial Differential Equations, to appear. | MR 1680893 | Zbl 0926.35064
,[STW] Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term, Indiana Univ. Math. J., Vol. 48, 3, 1996, pp. 655-682. | MR 1422101 | Zbl 0990.35061
, and ,[SW] Self-similar sub-solutions and blow-up for nonlinear parabolic equations, J. Math. Anal. Appl., Vol. 212, 1997, pp. 60-74. | MR 1460184 | Zbl 0892.35011
and ,[W] Semilinear evolution equations in Banach spaces, J. Functional Analysis, Vol. 32, 4, 1979, pp. 277-296. | MR 538855 | Zbl 0419.47031
,