Extinction and non-extinction of solutions for a nonlocal reaction-diffusion problem

We investigate extinction properties of solutions for the homogeneous Dirichlet boundary value problem of the nonlocal reaction-diffusion equation $u_t-d\Delta u+k u^p=\int_\Omega u^q(x,t)\,dx$ with $p, q\in (0, 1)$ and $k, d >0$. We show that $q=p$ is the critical extinction exponent. Moreover,...

Full description

Bibliographic Details
Main Author: Wenjun Liu
Format: Article
Language:English
Published: University of Szeged 2010-03-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=475
Description
Summary:We investigate extinction properties of solutions for the homogeneous Dirichlet boundary value problem of the nonlocal reaction-diffusion equation $u_t-d\Delta u+k u^p=\int_\Omega u^q(x,t)\,dx$ with $p, q\in (0, 1)$ and $k, d >0$. We show that $q=p$ is the critical extinction exponent. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.
ISSN:1417-3875
1417-3875