Thin front limit of an integro--differential Fisher--KPP equation with fat--tailed kernels

2017/05/31 by Émeric Bouin, Bouin, Emeric, Jimmy Garnier +5 · 1 citation
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1705.10997

openalex publication_date 2017/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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