Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion

Abstract

We consider here a model of accelerating fronts, 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 proposed in a previous work by H. Berestycki, L. Rossi and the authors, as a mechanism of front acceleration by a line of fast diffusion. In this latter work, it was indeed proved that the propagation in the direction of the line was exponentially fast in time. Inspired by numerical simulations of the first author, we make the estimate more precise by computing a time algebraic correction.

Keywords

• fisher-kpp
• front propagation
• line of nonlocal diffusion