10月29日 杜一宏教授学术报告(数学与统计学院)

作者:时间:2019-10-09浏览:11设置

报 告 人:杜一宏 教授

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

报告时间:2019年10月29日(周二)上午9:00-10:00

报告地点:静远楼204学术报告厅

主办单位:数学与统计学院、科学技术研究院

报告人简介:

  杜一宏,澳大利亚University of New England教授,博士生导师。于山东大学获得博士学位,师从郭大钧教授。随后分别赴英国Heriot-Watt University、澳大利亚University of New England担任Research Fellow,合作导师为国际著名数学家、澳大利亚科学院院士E.N. Dancer教授。目前主要研究领域包括非线性椭圆型和抛物型偏微分方程、自由边界问题、非线性泛函分析及其应用等。已在国际一流数学杂志包括JEMS、ARMA、PLMS、JFA、JMPA、TAMS、AIHP、SIAM、IUMJ、CVPDE、Nonlinearity、JDE等发表学术论文130余篇,并出版2部专著,且于2018年获Clarivate (Web of Science)高被引学者。多次组织国际性学术会议、担任国际大会执行和学术委员会委员。已连续6次主持澳大利亚国家研究基金(ARC)。目前担任多个国际期刊杂志的编委及20余种国际期刊杂志的审稿人。

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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