Different Asymptotic Spreading Speeds Induced by Advection in a Diffusion Problem with Free Boundaries

TL;DR

This paper investigates a Fisher-KPP model with advection and free boundaries, proving the existence of distinct positive asymptotic spreading speeds in opposite directions, which differ from the no-advection case.

Contribution

It introduces a novel analysis of asymmetric spreading speeds in a free boundary Fisher-KPP model with advection, revealing their relation to the no-advection scenario.

Findings

Existence of positive asymptotic spreading speeds in both directions.

One spreading speed exceeds and the other is less than the no-advection speed.

Asymmetric spreading speeds are influenced by the advection term.

Abstract

In this paper, we consider a Fisher-KPP equation with an advection term and two free boundaries, which models the behavior of an invasive species in one dimension space. When spreading happens (that is, the solution converges to a positive constant), we use phase plane analysis and upper/lower solutions to prove that the rightward and leftward asymptotic spreading speeds exist, both are positive constants. Moreover, one of them is bigger and the other is smaller than the spreading speed in the corresponding problem without advection term.