讲座题目：Propagation dynamics for time-periodic partially degenerate reaction-diffusion systems

主办单位：三峡数学研究中心/理学院

报告专家：吴事良 教授（西安电子科技大学大学）

报告时间：2021年12月1日（周三）  上午 9：00

报告地点：腾讯会议（ID： 870 654 209）

专家简介： 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。主持国家自然科学基金4项，获陕西省科学技术奖一等奖两项、第十一届陕西青年科技奖；获陕西省杰出青年基金资助。在相关领域的知名期刊，如Trans. Amer. Math. Soc.、SIAM J. Math Anal.、J. Differential equations、Proc. Amer. Math. Soc.、Nonlinearity、J. Dynam. Differential Equations、J. Nonlinear Science、European J. Appl. Math、Discrete Cont. Dyn. Systems、Proc. Royal Soc. Edinburgh (A)等发表论文多篇。

报告摘要： This talk is concerned with propagation dynamics for time-periodic partially degenerate reaction-diffusion systems with monostable nonlinearity. In the cooperative case, we prove the existence and exponential stability of the periodic traveling fronts. In the non-cooperative case, we establish the existence of the minimal wave speed of periodic traveling waves and show that it coincides with the spreading speed. More specifically, when the system is non-degenerate, the existence of the periodic traveling waves is proved by using the Schauder's fixed point theorem and regularity of analytic semigroup; while in the partially degenerate case, due to the lack of compactness and standard parabolic estimates, the existence result is obtained by appealing to the asymptotic fixed point theorem with the help of some properties of the Kuratowski measure of noncompactness. This is a joint work with Mingdi Huang and Xiao-Qiang Zhao.