We investigate extinction properties of solutions for the homogeneous Dirichlet boundary value problem of the nonlocal reaction-diffusion equation $u_t-dDelta u+k u^p=int_Omega u^q(x,t),dx$ with $p, qin (0, 1)$ 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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机译：我们研究了非局部反应扩散方程$ u_t-d Delta u + ku ^ p = int_ Omega u ^ q（x，t），dx $的齐次Dirichlet边值问题的解的灭性p，q in（0，1）$和$ k，d> 0 $。我们证明$ q = p $是关键的灭绝指数。此外，得出了在灭绝发生之前溶液的精确衰减估计。
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