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

主讲人：吴事良 西安电子科技大学教授

时间：2022年12月2日9：00

地点：腾讯会议 538 474 037

举办单位：数理学院

主讲人介绍：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。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。完成国家自然科学基金三项，在研国家自然科学基金面上项目和陕西省杰出青年科学基金各一项；获陕西省科学技术奖一等奖两项(分别为第二、第六完成人)、二等奖一项(第一完成人)，及第十一届陕西青年科技奖；入选首届年陕西省高等学校杰出青年人才计划。部分成果发表在J. Math Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math Anal.、J. Differential equations、Proc. Amer. Math. Soc.、Nonlinearity、J. Dynam. Differential Equations、J. Nonlinear Science等期刊。

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.