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11-20【李 芳】管研楼1418 The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries

发布者:万宏艳威尼斯官方网站:2020-11-19浏览次数:232

题目: The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries

报告人:李芳(中山大学)

时间: 2020年11月20日, 周五,14:00-15:00  

地点:管研楼1418

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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