报告人：吴事良（西安电子科技大学）

邀请人：李骥

报告时间：2022年11月3日（星期四）14:30-16:30

报告地点：腾讯会议：152 702 629

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

报告摘要：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.