Asymptotic spreading speed for the weak competition system with a free boundary

TL;DR

This paper investigates the long-term behavior of a diffusive competition system with a free boundary, establishing criteria for invasion success and deriving the asymptotic spreading speed of an invasive species.

Contribution

It provides sharp criteria for spreading and vanishing, and determines the asymptotic spreading speed involving complex traveling wave equations.

Findings

Spreading-vanishing dichotomy determines long-term outcomes.

Sharp criteria for invasion success or failure.

Explicit asymptotic spreading speed when invasion occurs.

Abstract

This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor. We show that the longtime dynamical behavior of the system is determined by a spreading-vanishing dichotomy, and provide sharp criteria for spreading and vanishing of the invasive species. Moreover, we determine the asymptotic spreading speed of the invasive species when its spreading is successful, which involves two systems of traveling wave type equations, and is highly nontrivial to establish.