Large Time Behavior of a Nonlocal Diffusion Equation with Absorption and Bounded Initial Data

Details Large Time Behavior of a Nonlocal Diffusion Equation with Absorption and Bounded Initial Data Large Time Behavior of a Nonlocal Diffusion Equation with Absorption and Bounded Initial Data

2010-04-05

arxiv.org/abs/1004.0717v2

Mathematics

Analysis of PDEs

Scientific paper

We study the large time behavior of nonnegative solutions of the Cauchy problem $u_t=\int J(x-y)(u(y,t)-u(x,t))\,dy-u^p$, $u(x,0)=u_0(x)\in L^\infty$, where $|x|^{\alpha}u_0(x)\to A>0$ as $|x|\to\infty$. One of our main goals is the study of the critical case $p=1+2/\alpha$ for $0<\alpha

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