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The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries
The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries
教师介绍

本讲教师:李芳
所属学科:理科
人  气:1141

课程介绍
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 [1] 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 [1]. 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. [1] Y. Du, Z. Lin, Spreading-Vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010) 377-405.
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