The extinction behavior of the solutions for a class of reaction-diffusion equations.
type: Item
instance of: scholarly article
title: The extinction behavior of the solutions for a class of reaction-diffusion equations.
zbMATH Open document ID: 1042.35024
DOI: 10.1023/A:1016394627496
author: Songlin Chen
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2001-01-01T00:00:00Z
review text: This paper is devoted to the following general problem with nonnegative initial and homogeneous Dirichlet boundary values \[ \begin{cases} \frac{\partial u}{\partial t}=\Delta u-\lambda| u|^{\gamma-1}u-\beta u,\;(x,t)\in\Omega\times(0,+\infty)\\ u(x,t)|_{\partial\Omega\times(0,+\infty)}=0\\ u(x,0)=u_0(x)\in H^1_0(\Omega)\cap L^{1+\gamma}(\Omega),\end{cases}\tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N(N\geq 2)\) with smooth boundary, \(\lambda,\beta,\gamma\) are positive parameters. The author presents sufficient and necessary conditions about extinction of solutions of (1). Note that this problem can be viewed as mathematical model of chemotaxis system. Moreover the author indicates and discusses the possibility of an approach developed in this paper to higher-order equation.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 1743651
zbMATH Keywords: criteria for extinction of solution
zbMATH Keywords: nonnegative initial data
zbMATH Keywords: chemotaxis system
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1016394627496
OpenAlex ID: W4229509429
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description: scientific article; zbMATH DE number 1743651