The Dynamics of a Lotka-Volterra competition model with nonlocal diffusion and free boundaries

Abstract

This paper is concerned with a Lotka-Volterra competition model with nonlocal diffusion and free boundaries, which describes the evolution of an invasive species with free boundaries in a one-dimensional habitat and a native species in the whole space. We prove the well-posedness of the model and obtain a spreading-vanishing dichotomy for the invasive species. Sharp criteria for spreading and vanishing are also obtained, which reveal significant differences from the local model. Depending on the choice of the kernel function in the nonlocal diffusion operator, it is expected that the nonlocal model here may have accelerated spreading, which would contrast sharply to the local model, where the spreading has finite speed whenever spreading happens.