Decay of mass for nonlinear equation with fractional Laplacian

Abstract

The large time behavior of nonnegative solutions to the reaction-diffusion equation ${\partial }_{t}u=-(-\Delta {)}^{\alpha /2}u-u^p,$ $(\alpha \in (0,2],p>1)$ posed on ${\mathbb{R}}^N$ and supplemented with an integrable initial condition is studied. We show that the anomalous diffusion term determines the large time asymptotics for $p>1+\alpha /N,$ while nonlinear effects win if $p\le 1+\alpha /N.$

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