Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations
Analysis of PDEs
2011-11-03 v1
Abstract
We study the Fisher-KPP equation with a fractional laplacian of order {\alpha} \in (0, 1). We know that the stable state invades the unstable one at constant speed for {\alpha} = 1, and at an exponential in time velocity for {\alpha} \in (0, 1). The transition between these two different speeds is examined in this paper. We prove that during a time of the order - ln(1 - {\alpha}), the propagation is linear and then it is exponential.
Keywords
Cite
@article{arxiv.1111.0408,
title = {Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations},
author = {Anne-Charline Coulon and Jean-Michel Roquejoffre},
journal= {arXiv preprint arXiv:1111.0408},
year = {2011}
}