Title: Front propagation in Fisher-KPP equations with fractional diffusion
Authors: Xavier Cabre, Jean-Michel Roquejoffre
(Submitted on 8 May 2009)

    Abstract: 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.