Asymptotic behavior of solutions for partial differential equations with degenerate diffusion and logistic reaction

S. Takeuchi

doi:10.1016/S0362-546X(01)00304-2

Asymptotic behavior of solutions for partial differential equations with degenerate diffusion and logistic reaction

Research output: Contribution to journal › Conference article › peer-review

Abstract

Global existence and asymptotic behavior of solutions for degenerate parabolic equations including u_t = 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	https://doi.org/10.1016/S0362-546X(01)00304-2
Publication status	Published - 2001 Aug 1
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

Access to Document

10.1016/S0362-546X(01)00304-2

Fingerprint Dive into the research topics of 'Asymptotic behavior of solutions for partial differential equations with degenerate diffusion and logistic reaction'. Together they form a unique fingerprint.

Cite this

@article{5d0d59b61098488fb63f1a2996e8c123,

title = "Asymptotic behavior of solutions for partial differential equations with degenerate diffusion and logistic reaction",

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.",

keywords = "Asymptotic behavior, Degenerate parabolic equations, Logistic reaction, Stability, p-Laplacian",

author = "S. Takeuchi",

year = "2001",

month = aug,

day = "1",

doi = "10.1016/S0362-546X(01)00304-2",

language = "English",

volume = "47",

pages = "1715--1724",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Limited",

number = "3",

note = "3rd World Congress of Nonlinear Analysts ; Conference date: 19-07-2000 Through 26-07-2000",

}

TY - JOUR

T1 - Asymptotic behavior of solutions for partial differential equations with degenerate diffusion and logistic reaction

AU - Takeuchi, S.

PY - 2001/8/1

Y1 - 2001/8/1

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

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 - 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 -