2015/06/30 by Henri Berestycki, Berestycki, Henri, Anne-Charline Coulon +6 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics #math.AP
paper · pdf · doi:10.48550/arxiv.1506.09046
arxiv created 2015/06/30 · openalex publication_date 2015/06/30 · arxiv updated 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose here a new model of accelerating fronts, consisting of one equation with non-local diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation in the upper half-plane. The underlying biological question is to understand how transportation networks may enhance biological invasions. We show that the line accelerates the propagation in the direction of the line and enhances the overall propagation in the plane and that the propagation is directed by diffusion on the line, where it is exponentially fast in time. We also describe completely the invasion in the upper half-plane. This work is a non-local version of the model introduced in [Berestycki-Roquejoffre-Rossi 2013], where the line had a strong but local diffusion described by the classical Laplace operator.