The effect on Fisher-KPP propagation in a cylinder with fast diffusion on the boundary

TL;DR

This paper investigates how reaction-diffusion processes of Fisher-KPP type propagate in an infinite cylindrical domain with boundary conditions allowing fast diffusion, analyzing the asymptotic speed's dependence on boundary diffusivity and domain size.

Contribution

It introduces a coupled reaction-diffusion model in cylindrical domains with boundary fast diffusion and studies the asymptotic propagation speed.

Findings

Existence of an asymptotic propagation speed for the system.

Dependence of the speed on boundary diffusivity and domain amplitude.

Modeling of fast diffusion effects in strip-shaped fields with roads.

Abstract

In this paper we consider a reaction-diffusion equation of Fisher-KPP type inside an infinite cylindrical domain in $\mathbb{R}^{N+1}$, coupled with a reaction-diffusion equation on the boundary of the domain, where potentially fast diffusion is allowed. We will study the existence of an asymptotic speed of propagation for solutions of the Cauchy problem associated with such system, as well as the dependence of this speed on the diffusivity at the boundary and the amplitude of the cylinder. When $N=1$ the domain reduces to a strip between two straight lines. This models the effect of two roads with fast diffusion on a strip-shaped field bounded by them.