报告题目：Propagation Phenomena for a Two-Species Lotka-Volterra Strong Competition System with Nonlocal Dispersal

报 告 人：张国宝 教授 西北师范大学

照    片：

邀 请 人：吴事良

报告时间：2020年10月22日（周四） 14：30-15：30

腾讯会议ID：612 812 542

报告人简介：张国宝，西北师范大学williamhill威廉希尔官网教授，博士生导师。2011年在兰州大学获得理学博士学位。2012年10月-2015年10月在西北师范大学数学博士后流动站做博士后。2018年4月-2019年3月在加拿大纽芬兰纪念大学做博士后。现为美国《Math. Review》评论员和德国《Zentralblatt MATH》评论员。

主要研究方向为微分方程及其应用。主持国家自然科学基金3项，省部级基金4项；获甘肃省自然科学奖一等奖一项，甘肃省高校科技进步奖一等奖2项；发表学术论文30余篇，其中多篇论文发表在国际、国内权威杂志《Calculus of Variations and PDE》、《J. Differential Equations》、《Z. Angew. Math. Phys.》、《Discrete Contin. Dyn. Syst. A&B》、《Nonlinear Anal. RWA.》、《Nonlinear Anal.》、《J. Math. Anal. Appl.》、《J. Comput. Appl. Math.》和《Sci. China Math.》。

报告摘要：We consider the propagation phenomena for a two-species Lotka-Volterra strong competition system with nonlocal dispersal. We first establish the existence of bistable traveling waves by appealing to the theory of monotone semiflows. Then we use a dynamical systems approach to prove that such a bistable traveling wave is asymptotically stable and unique modulo translation. Finally, we study the spreading properties of solutions for a class of initial conditions by the comparison arguments and the methods of super- and subsolutions. It is shown that for initial conditions where both species u and v are initially absent from the right half-line x > 0, and the species v dominates the species u around x=-∞ initially, if v spreads in absence of u slower than u in absence of v, then solutions of initial value problem will approach a propagating terrace, which connects the unstable state (0,0) to the stable state (1, 0), and then the stable state (1,0) to the other stable state (0,1).