Monatshefte für Mathematik

, Volume 160, Issue 4, pp 375–384

Decay of mass for nonlinear equation with fractional Laplacian

Authors

  • Ahmad Fino
    • Laboratoire MIA et Département de MathématiquesUniversité de La Rochelle
    • LaMA-LibanLebanese University
    • Instytut MatematycznyUniwersytet Wrocławski
Article

DOI: 10.1007/s00605-009-0093-3

Cite this article as:
Fino, A. & Karch, G. Monatsh Math (2010) 160: 375. doi:10.1007/s00605-009-0093-3
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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 solutionsFractional LaplacianBlow-up of solutionsCritical exponent

Mathematics Subject Classification (2000)

Primary 35K55Secondary 35B4060H99

Copyright information

© Springer-Verlag 2009