Decay of mass for nonlinear equation with fractional Laplacian

Details Decay of mass for nonlinear equation with fractional Laplacian Decay of mass for nonlinear equation with fractional Laplacian

2008-12-29

arxiv.org/abs/0812.4977v1

Mathematics

Analysis of PDEs

Scientific paper

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 $p\leq1+{\alpha}/{N}.$

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