报告题目：Long time behavior for a periodic Lotka-Volterra reaction-diffusion system with strong competition 

报告时间：2023年10月26日 8:50-

报告人： 吴事良 教授， 西安电子科技大学

报告地点：腾讯会议，会议号：754-111-413

摘要： This talk is concerned with the long time behavior of bounded solutions to a two-species time-periodic Lotka-Volterra reaction-diffusion system with strong competition. It is well known that solutions of the Cauchy problem of this system with front-like initial values converge to a bistable periodic traveling front. One may ask naturally how solutions of such time-periodic systems with other types of initial data evolve as time increases. By transforming the system into a cooperative system on [(0,0),(1,1)], we first show that if the bounded initial value has compact support and equals (1,1) for a sufficiently large x-level, then solutions converge to a pair of diverging periodic traveling fronts. As a by-product, we obtain a sufficient condition for solutions to spread to (1,1). We also prove that if the two species are initially absent from the right half-line x>0 and the slower one dominates the faster one on x<0, then solutions approach a propagating terrace, which means that several invasion speeds can be observed.

报告人简介： 西安电子科技大学yl23455永利教授，博士生导师，中国数学会理事和陕西省数学会常务理事。研究方向为微分方程、动力系统及生物应用。部分成果发表在J. Math. Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math. Anal.、Calc. Var. PDE、J. Differential equations、Nonlinearity、J. Dynam. Differential Equations、J. Nonlinear Science等期刊。获2017年陕西省科学技术奖一等奖(第二完成人)、2022年陕西省科学技术奖二等奖(第一完成人)以及第十一届陕西青年科技奖。主持完成陕西省杰出青年科学基金和国家自然科学基金面上项目各一项，正在主持一项国家自然科学基金面上项目。