Abstract

We consider a class of partially degenerate nonlocal diffusion systems with free boundaries. Such problems can describe the evolution of one species with nonlocal diffusion and the other without diffusion or with much slower diffusion. The existence, uniqueness, and regularity of global solutions are first proven. The criteria of spreading and vanishing are also established for the Lotka-Volterra type competition and prey-predator growth terms. Moreover, we investigate long-time behaviors of the solution and propose estimates of spreading speeds when spreading occurs.

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