A reaction-diffusion-advection competition model with two free boundaries in heterogeneous time-periodic environment

TL;DR

This paper analyzes a two-species competition model with free boundaries in a heterogeneous, time-periodic environment, incorporating movement and advection, and classifies its long-term dynamics into four distinct cases.

Contribution

It introduces a novel reaction-diffusion-advection model with free boundaries in a time-periodic environment and provides criteria for spreading and vanishing behaviors.

Findings

Classified the model's dynamics into four cases

Established estimates for spreading speed and long-term behavior

Provided conditions for species spreading and vanishing

Abstract

In this paper, we study the dynamics of a two-species competition model with two different free boundaries in heterogeneous time-periodic environment, where the two species adopt a combination of random movement and advection upward or downward along the resource gradient. We show that the dynamics of this model can be classified into four cases, which forms a spreading-vanishing quartering. The notion of the minimal habitat size for spreading is introduced to determine if species can always spread. Rough estimates of the asymptotic spreading speed of free boundaries and the long time behavior of solutions are also established when spreading occurs. Furthermore, some sufficient conditions for spreading and vanishing are provided.