Propagation dynamics for time-periodic partially degenerate reaction-diffusion systems

主讲人：吴事良  西安电子科大教授

时间：2021年12月8日19：30

地点：腾讯会议 456 488 324

举办单位：数理学院

主讲人介绍：吴事良，西安电子科技大学教授，博士生导师。2013至2014年于美国迈阿密大学数学系公派访问。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项以及陕西省杰出青年基金，获陕西省科学技术奖一等奖两项、陕西省优秀博士学位论文奖以及第十一届陕西青年科技奖。在相关领域的国内外期刊，如Trans.  Amer. Math. Soc.、SIAM J. Math. Anal.、J. Differential equations、Proc. Amer. Math.  Soc.、Nonlinearity、J. Dynam. Differential Equations、J. Nonlinear Science、Proc.  Royal Soc. Edinburgh (A)与数学年刊等发表论文30余篇。

内容介绍：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.