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,...
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| Format: | Article |
| Language: | English |
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University of Szeged
2010-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=475 |
| 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. |
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| ISSN: | 1417-3875 1417-3875 |