2019/11/08 by Anne-Charline Chalmin, Jean‐Michel Roquejoffre, Chalmin, Anne-Charline +1
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.1911.03239
openalex publication_date 2019/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper half-plane. It was proved in [2] that the propagation is accelerated in the direction of the line exponentially fast in time. We make this estimate more precise by computing an explicit correction that is algebraic in time. Unexpectedly, the solution mimicks the behaviour of the solution of the equation linearised around the rest state 0 in a closer way than in the classical fractional Fisher-KPP model.