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

Wenjun Liu, Nanjing University of Information Science and Technology, Nanjing, P. R. China.

E. J. Qualitative Theory of Diff. Equ., No. 15. (2010), pp. 1-12.

Abstract: 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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