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

2010/04/05 by Terra, Joana, Wolanski, Noemi · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1004.0717

Abstract

We study the large time behavior of nonnegative solutions of the Cauchy problem u_t=∫ J(x-y)(u(y,t)-u(x,t)) dy-u^p, u(x,0)=u₀(x)∈ L^∞, where |x|^αu₀(x)→ A>0 as |x|→∞. One of our main goals is the study of the critical case p=1+2/α for 0

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