Propagation in Fisher-KPP type equations with fractional diffusion in periodic media

2012/09/21 by Xavier Cabré, Cabre, Xavier, Anne-Charline Coulon +3
Mathematics · Medicine · #35K57 Reaction-diffusion equations #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1209.4809

openalex publication_date 2012/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in the time asymptotic location of the level sets of solutions to Fisher-KPP reaction-diffusion equations with fractional diffusion in periodic media. We show that the speed of propagation is exponential in time, with a precise exponent depending on a periodic principal eigenvalue, and that it does not depend on the space direction. This is in contrast with the Freidlin-Gärtner formula for the standard Laplacian.

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