Free boundary problems of the competition model with sign-changing coefficients in heterogeneous time-periodic environment

TL;DR

This paper investigates a diffusive competition model with free boundaries in a heterogeneous, time-periodic environment where growth rates can change signs, establishing conditions for species spread or extinction and analyzing their long-term behavior.

Contribution

It introduces a novel analysis of a competition model with sign-changing coefficients in a time-periodic setting, providing criteria for spreading and vanishing.

Findings

Established a spreading-vanishing dichotomy for the species.

Derived sharp criteria for species spreading and extinction.

Estimated the asymptotic spreading speed of the free boundary.

Abstract

In this paper we consider the diffusive competition model with free boundary in the heterogeneous time-periodic environment, in which the variable intrinsic growth rates of invasive and native species may change signs and be "very negative" in a "suitable large region" . The main objective is to understand the asymptotic behavior of the two competing species spreading via a free boundary. We first establish a spreading-vanishing dichotomy, namely the two species either successfully spread to the right-half-space as time $t$ goes to infinity and survive in the new environment, or they fail to establish and will extinct in the long run. Then we study the long time behavior of solution, sharp criteria for spreading and vanishing, and estimate of the asymptotic spreading speed of the free boundary.