Decay of mass for nonlinear equation with fractional Laplacian

Ahmad Fino; Grzegorz Karch

Decay of mass for nonlinear equation with fractional Laplacian

Analysis of PDEs 2008-12-31 v1

Authors: Ahmad Fino , Grzegorz Karch

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

Keywords

fractional laplacian reaction-diffusion equation large time behavior mass decay anomalous diffusion

Cite

@article{arxiv.0812.4977,
  title  = {Decay of mass for nonlinear equation with fractional Laplacian},
  author = {Ahmad Fino and Grzegorz Karch},
  journal= {arXiv preprint arXiv:0812.4977},
  year   = {2008}
}

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