Monatshefte für Mathematik

, Volume 160, Issue 4, pp 375–384

Decay of mass for nonlinear equation with fractional Laplacian

Article

Abstract

The large time behavior of non-negative 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 + α/N, while nonlinear effects win if p ≤ 1 + α/N.

Keywords

Large time behavior of solutions Fractional Laplacian Blow-up of solutions Critical exponent 

Mathematics Subject Classification (2000)

Primary 35K55 Secondary 35B40 60H99 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Laboratoire MIA et Département de MathématiquesUniversité de La RochelleLa Rochelle CedexFrance
  2. 2.LaMA-LibanLebanese UniversityTripoliLebanon
  3. 3.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland

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