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.
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版ステータス||Published - 2001 8|
|イベント||3rd World Congress of Nonlinear Analysts - Catania, Sicily, Italy|
継続期間: 2000 7 19 → 2000 7 26
ASJC Scopus subject areas
- Applied Mathematics