%0 Journal Article
%T Decay of mass for nonlinear equation with fractional Laplacian
%A Ahmad Fino
%A Grzegorz Karch
%J Mathematics
%D 2008
%I arXiv
%X 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 $p\leq1+{\alpha}/{N}.$
%U http://arxiv.org/abs/0812.4977v1