Dynamics of a nonlocal diffusive logistic model with free boundaries in time periodic environment

Abstract

In this paper we study a nonlocal diffusion model with double free boundaries in time periodic environment, which is the natural extension of the free boundary model in [ 17 ], where local diffusion is used to describe the population dispersal. We give the existence and uniqueness of global solution and consider the properties of principle eigenvalue of time-periodic parabolic-type eigenvalue problem. With the help of attractivity of time periodic solutions, we establish a spreading-vanishing dichotomy. The sharp criteria for spreading and vanishing are also obtained.