数学科学学院学术报告[2024] 002号

(高水平大学建设系列报告882号)

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

报告人：吴事良 教授（西安电子科技大学）

报告时间：2024年1月12日下午14:30-15:30

报告地点：科技楼514

报告内容：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：吴事良，西安电子科技大学数学与统计学院教授，博士生导师。现为中国数学会理事和陕西省数学会常务理事。主要研究方向为微分方程、动力系统及应用。完成国家自然科学基金三项和陕西省杰出青年科学基金一项，在研国家自然科学基金面上项目一项；获陕西省科学技术奖一等奖两项、二等奖一项(第一完成人)、第十一届陕西青年科技奖。部分成果发表在J. Math Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math Anal.、Calc. Var. Partial Differential Equations、J. Differential equations、Nonlinearity、J. Dynam. Differential Equations、J. Nonlinear Science等期刊。目前担任SCI期刊International Journal of Biomathematics的编委。

报告邀请人：叶海龙

数学科学学院

2024年01月11日