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 |
|---|---|
| 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 |
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Keywords
- Asymptotic behavior
- Degenerate parabolic equations
- Logistic reaction
- p-Laplacian
- Stability
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Mathematics(all)
Cite this
Asymptotic behavior of solutions for partial differential equations with degenerate diffusion and logistic reaction. / Takeuchi, Shingo.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 47, No. 3, 08.2001, p. 1715-1724.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotic behavior of solutions for partial differential equations with degenerate diffusion and logistic reaction
AU - Takeuchi, Shingo
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 - p-Laplacian
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=0035424378&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035424378&partnerID=8YFLogxK
U2 - 10.1016/S0362-546X(01)00304-2
DO - 10.1016/S0362-546X(01)00304-2
M3 - 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
ER -