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References (9)
-
M. Escobedo, M. Herrero (1993)
A semilinear parabolic system in a bounded domainAnnali di Matematica Pura ed Applicata, 165
-
M. Tsutsumi (1972)
Existence and Nonexistence of Global Solutions for Nonlinear Parabolic EquationsPublications of The Research Institute for Mathematical Sciences, 8
-
O. Ladyženskaja (1968)
Linear and Quasilinear Equations of Parabolic Type, 23
-
M. Nakao (1986)
Global solutions for some nonlinear parabolic equations with nonmonotonic peturbationsNonlinear Analysis-theory Methods & Applications, 10
-
Y. Ohara (1992)
L ∞ -estimates of solutions of some nonlinear degenerate parabolic equationsNonlinear Analysis-theory Methods & Applications, 18
-
E. DiBenedetto (1993)
Degenerate Parabolic Equations -
N. Alikakos, R. Rostamian (1982)
Gradient estimates for degenerate diffusion equations. IMathematische Annalen, 259
-
Chen Cai-sheng, Wang Ru-yun (2002)
L ∞ estimates of solution for the evolution m-Laplacian equation with initial value in L q (ω)Nonlinear Analysis-theory Methods & Applications, 48
-
Hongwei Chen (1997)
Global Existence and Blow-up for a Nonlinear Reaction-Diffusion System☆Journal of Mathematical Analysis and Applications, 212
- Publisher
- Springer Journals
- Copyright
- Copyright © 2006 by Birkhäuser Verlag, Basel
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-005-0210-2
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we study the global existence, L ∞ estimates and decay estimates of solutions for the quasilinear parabolic system u t = div (|∇ u | m ∇ u ) + f ( u , v ), v t = div (|∇ v | m ∇ v ) + g ( u , v ) with zero Dirichlet boundary condition in a bounded domain Ω ⊂ R N . In particular, we find a critical value for the existence and nonexistence of global solutions to the equation u t = div (|∇ u | m ∇ u ) + λ | u | α - 1 u .
Journal
Journal of Evolution Equations – Springer Journals
Published: Feb 1, 2006