Propagation speed in a strip bounded by a line with different diffusion

TL;DR

This paper investigates how the presence of a road with different diffusion properties affects the speed of population spread in a strip-shaped habitat, revealing increased propagation speeds and asymptotic behaviors as the strip widens.

Contribution

It establishes the existence of an asymptotic propagation speed influenced by the road and analyzes its limits for varying diffusion coefficients and strip widths.

Findings

Propagation speed exceeds the no-road case.

Speed approaches the half-plane limit as strip width increases.

Behavior characterized for small and large diffusion on the road.

Abstract

In this paper we consider a model for the diffusion of a population in a strip-shaped field, where the growth of the species is governed by a Fisher-KPP equation and which is bounded on one side by a road where the species can have a different diffusion coefficient. Dirichlet homogeneous boundary conditions are imposed on the other side of the strip. We prove the existence of an asymptotic speed of propagation which is greater than the one of the case without road and study its behavior for small and large diffusions on the road. Finally we prove that, when the width of the strip goes to infinity, the asymptotic speed of propagation approaches the one of an half-plane bounded by a road, case that has been recently studied in [2],[3].