TY - JOUR
T1 - Asymptotic behavior of solutions for partial differential equations with degenerate diffusion and logistic reaction
AU - Takeuchi, S.
N1 - Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.
PY - 2001/8
Y1 - 2001/8
N2 - 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.
AB - 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.
KW - Asymptotic behavior
KW - Degenerate parabolic equations
KW - Logistic reaction
KW - Stability
KW - p-Laplacian
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U2 - 10.1016/S0362-546X(01)00304-2
DO - 10.1016/S0362-546X(01)00304-2
M3 - Conference article
AN - SCOPUS:0035424378
VL - 47
SP - 1715
EP - 1724
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 3
T2 - 3rd World Congress of Nonlinear Analysts
Y2 - 19 July 2000 through 26 July 2000
ER -