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Propagation Dynamics of Asymmetric Nonlocal Dispersal Equations
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报告题目:Propagation Dynamics of Asymmetric Nonlocal Dispersal Equations
    报告人:李万同 教授  兰州大学

 

邀请人:吴事良 教授、常永奎 教授
    报告时间:6月1日15:30-16:30
    报告地点:信远楼II206数统院报告厅

报告人简介:  李万同,二级教授,博导,兰州大学“萃英学者”特聘教授。研究方向为偏微分方程与动力系统。目前任兰州大学数学与统计学院院长,甘肃省应用数学与复杂系统省级重点实验室主任,中国数学会常务理事,甘肃省数学会理事长。2013年应邀在第六届世界华人数学家大会做邀请报告。先后连续三次入选2014至2016年全球“最具影响力科学精英”榜单,并被授予“高被引科学家奖”。2009年入选甘肃省领军人才第一层次,2004年享受国务院政府特殊津贴并获“教育部宝钢教育基金会优秀教师奖”,2001年获教育部“高等学校青年教师奖”,并被甘肃省人民政府授予“甘肃省优秀专家”。先后主持国家自然科学基金重点及面上项目7项,参加重点项目1项。合作在Marcel Dekker出版社《纯粹数学与应用数学专著系列》第267卷出版英文专著一部,先后在《TAMS》、《JMPA》、 《SIAM JMA》、 《JDE》等期刊发表SCI论文百余篇,被SCI引用4400余次。获甘肃省自然科学一等奖1项、二等奖2项。

报告摘要:This talk is concerned with entire solutions of the asymmetric nonlocal dispersal equation $u_t=J*u-u+f(u)$ with monostable, bistable and ignition nonlinearity, respectively, where the kernel function $J$ is asymmetric. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more different types of entire solutions since it can affect the range and sign of the wave speeds, which further leads to o symmetry between the corresponding nonincreasing and nondecreasing waves. For the KPP, bistable and ignition nonlinearities, We establish respectively some new entire solutions and obtain its qualitative properties by constructing proper supersolution and subsolution and by classifying the sign and size of the wave speeds. In particular, if $f$ is the KPP nonlinear term and the kernel $J$ is symmetric, then the entire solutions are proved to be 5-dimensional, 4-dimensional, and 3-dimensional manifolds, respectively.This is the joint work with Yu-Juan Sun, Zhi-Cheng Wang and Li Zhang.

 

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