The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries
摘要：We introduce and study a class of free boundary models with ``nonlocal diffusion'', which are natural extensions of the free boundary models in  and elsewhere, where ``local diffusion'' is used to describe the population dispersal, with the free boundary representing the spreading front of the species. We show that this nonlocal problem has a unique solution defined for all time, and then examine its long-time dynamical behavior when the growth function is of Fisher-KPP type. We prove that a spreading-vanishing dichotomy holds, though for the spreading-vanishing criteria significant differences arise from the well known local diffusion model in . Furthermore, we establish a threshold condition on the kernel function such that spreading grows linearly in time exactly when this condition holds, while when the kernel function violates this condition, accelerating spreading happens.  Y. Du, Z. Lin, Spreading-Vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010) 377-405.