Decay of mass for nonlinear equation with fractional Laplacian

2008/12/29 by Fino, Ahmad, Karch, Grzegorz · 2 citations
#35B40 #35K55 #60H99 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0812.4977

Abstract

The large time behavior of nonnegative solutions to the reaction-diffusion equation ∂_t u=-(-Δ)^α/2u - u^p, (α∈(0,2], p>1) posed on ℝ^N and supplemented with an integrable initial condition is studied. We show that the anomalous diffusion term determines the large time asymptotics for p>1+α/N, while nonlinear effects win if p≤1+α/N.

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