Long-Time Dynamics of a Competition Model with Nonlocal Diffusion and Free Boundaries: Vanishing and Spreading of the Invader

In this work, we investigate the long-time dynamics of a two species competition model of Lotka-Volterra type with nonlocal diffusions. One of the species, with density v(t, x), is assumed to be a native in the environment (represented by the real line R), while the other species, with density u(t, x), is an invading species which invades the territory of v with two fronts, x = g(t) on the left and x = h(t) on the right.