Thin front limit of an integro--differential Fisher--KPP equation with fat--tailed kernels
Analysis of PDEs
2018-04-23 v2
Abstract
We study the asymptotic behavior of solutions to a monostable integro-differential Fisher-KPP equation , that is where the standard Laplacian is replaced by a convolution term, when the dispersal kernel is fat-tailed. We focus on two different regimes. Firstly, we study the long time/long range scaling limit by introducing a relevant rescaling in space and time and prove a sharp bound on the (super-linear) spreading rate in the Hamilton-Jacobi sense by means of sub-and super-solutions. Secondly, we investigate a long time/small mutation regime for which, after identifying a relevant rescaling for the size of mutations, we derive a Hamilton-Jacobi limit.
Keywords
Cite
@article{arxiv.1705.10997,
title = {Thin front limit of an integro--differential Fisher--KPP equation with fat--tailed kernels},
author = {Emeric Bouin and Jimmy Garnier and Christopher Henderson and Florian Patout},
journal= {arXiv preprint arXiv:1705.10997},
year = {2018}
}