A Nonlocal Diffusion Problem With Free Boundaries In Heterogeneous Environment

In this paper,we study the population dynamics of an invasive species in heterogeneous environment which is modeled by a nonlocal diffusion Logistic e-quation with free boundaries condition.First of all,we use a parametrized ODE problem and contraction mapping principle and extension method to obtain the global existence and uniqueness of the solution.Then,we consider the effect of the dispersal rate d and expansion ability ? on the population invasion in two cas-es:strong heterogeneous environment and weak heterogeneous environment.We derive sufficient conditions for species spreading(resp.vanishing)in the strong het-erogeneous environment;while in the weak heterogeneous environment,we obtain sharp criteria for the spreading and vanishing.