The influence of fractional diffusion in Fisher-KPP equations

Details The influence of fractional diffusion in Fisher-KPP equations The influence of fractional diffusion in Fisher-KPP equations

2012-02-27

arxiv.org/abs/1202.6072v1

Mathematics

Analysis of PDEs

Scientific paper

We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the stan- dard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable L\'evy process, the front position is exponential in time. Our results provide a mathe- matically rigorous justification of numerous heuristics about this model.

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