Abstract

In this paper, we mainly consider a class of free boundary problems of reaction-diffusion equations with nonlocal diffusion coefficient. By the well-known contraction mapping theorem, the uniqueness and existence of solutions are established for the local time t>0. Secondly, we give some sufficient conditions for vanishing phenomenon and spreading phenomenon, respectively. Further, we prove a spreading-vanishing dichotomy for this model. Finally, we obtain the asymptotic spreading speed when spreading happens.

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