A nonlocal diffusion competition model with seasonal succession and free boundaries

Abstract

In this paper, we investigate a nonlocal diffusion competition model with seasonal succession and free boundaries, which can be used to describe the dynamics of two species in an environment alternating between bad and good seasons. We first show the existence and uniqueness of global solution, and then focus on the long time behaviors of two species, namely, if h∞−g∞<∞ (the two species cannot spread over R), then they must die out in the long run; If h∞=−g∞=∞ (the two species spread to infinity as t→∞ at both fronts and survives in the new environment), then they must tend to the unique positive time periodic solution. Moreover, some sufficient conditions for spreading and vanishing are also given.