Abstract
Global existence and asymptotic behavior of solutions for degenerate parabolic equations including ut = λ div (|∇u|p-2 ∇u) + |u|q-2u(1 - |u|r) are studied, where λ is a positive parameter; p > 2, q ≥ 2 and r > 0 are constants. In particular, the behavior of solutions for the initial data close to a maximal stationary solution is discussed. It is shown that the maximal stationary solution is asymptotically stable if p ≥ q and stable if p < q. For the latter case, some remarks on the attractivity of maximal stationary solution are also given.
Original language | English |
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Pages (from-to) | 1715-1724 |
Number of pages | 10 |
Journal | Nonlinear Analysis, Theory, Methods and Applications |
Volume | 47 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2001 Aug |
Externally published | Yes |
Event | 3rd World Congress of Nonlinear Analysts - Catania, Sicily, Italy Duration: 2000 Jul 19 → 2000 Jul 26 |
Keywords
- Asymptotic behavior
- Degenerate parabolic equations
- Logistic reaction
- Stability
- p-Laplacian
ASJC Scopus subject areas
- Analysis
- Applied Mathematics