The influence of fractional diffusion in Fisher-KPP equations
Analysis of PDEs
2015-06-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1202.6072,
title = {The influence of fractional diffusion in Fisher-KPP equations},
author = {Xavier Cabre and Jean-Michel Roquejoffre},
journal= {arXiv preprint arXiv:1202.6072},
year = {2015}
}