报告题目：Dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries

报告人: Professor Yihong Du, University of New England, Australia

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邀请人：吴事良

报告时间：2019年11月4号15：30-16：30

报告地点：信远楼II区205

报告人简介：杜一宏， 1978-1988年在山东大学数学系攻读本科、硕士、博士学位，1988年获得博士学位，并留山东大学工作；1990年赴英国Heriot-Watt大学访问，1991年至今在澳大利亚新英格兰大学工作，现为该校理工学院教授。杜一宏教授是非线性泛函分析、偏微分方程及其应用等领域的国际知名专家。在Arch. Rational Mech. Anal., SIAM J. Math. Anal., J. Funct. Anal., J. European Math. Soc., Trans. Amer. Math. Soc., J. Differ. Equations, Calc. Var. Partial Differ. Equ., J. Math. Pures Appl. 等国际知名期刊上发表论文140余篇（他引2000余次），并出版专著2部。自2003年持续获得澳大利亚国家自然科学基金的资助，自2013年任澳大利亚国家自然科学基金委评审专家。目前，担任多种国际期刊杂志的编委及20余种国际期刊杂志的特约审稿人。

报告摘要：We introduce and discuss a class of free boundary problems with "nonlocal diffusion", which are natural extensions of the free boundary models considered by Du and Lin [SIAM J. Math. Anal., 2010] and elsewhere, where "local diffusion" was used to describe the dispersal of the species being modeled, 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 demonstrate that a spreading-vanishing dichotomy holds, though the spreading-vanishing criteria differ significantly from the well-known local diffusion model. The spreading speed is also determined, and unlike the corresponding local diffusion model, here accelerated spreading can happen. This talk is based on joint works with Cao JiaFeng, Li Fang, Li WanTong and Zhou MaoLin.

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