arXiv:0905.1299 Abstract | arXiv Analytics

arXiv:0905.1299 [math.AP]Abstract References Reviews Resources

Front propagation in Fisher-KPP equations with fractional diffusion

Published 2009-05-08Version 1

We study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fractional Laplacian. Contrary to what happens in the standard Laplacian case, where the stable state invades the unstable one at constant speed, we prove here that invasion holds at an exponential in time velocity. These results provide a mathematically rigorous justification of numerous heuristics about this model.

Categories: math.AP

Keywords: fisher-kpp equation, fractional diffusion, front propagation, standard laplacian case, fractional laplacian

Related articles: Most relevant | Search more

arXiv:1202.6072 [math.AP] (Published 2012-02-27)

The influence of fractional diffusion in Fisher-KPP equations

Xavier Cabre, Jean-Michel Roquejoffre

arXiv:1904.04593 [math.AP] (Published 2019-04-09)

On the KPZ equation with fractional diffusion

Boumediene Abdellaoui, Ireneo Peral, Ana Primo

arXiv:1405.4746 [math.AP] (Published 2014-05-19)

Singular limits for reaction-diffusion equations with fractional Laplacian and local or nonlocal nonlinearity

Sylvie Méléard, Sepideh Mirrahimi