Front propagation dynamics in Fisher KPP equations on unbounded metric graphs

主讲人：Wenxian Shen，Professor at Auburn University

时间：2025年5月28日9:30

地点：徐汇校区三号楼332室

举办单位：数理学院

主讲人介绍：沈文仙教授为国际知名微分方程动力系统专家，多年来致力于研究微分方程中的动力学问题，包括异质和随机介质理论中的行波解，单调动力系统中的Lyapunov指数理论，非局部扩散算子的谱理论及应用，拟周期反应扩散方程的渐近动力学行为，特别是与其合作者所发展的非自治单调斜积半流理论已成为处理许多非自治方程动力系统的重要工具。沈文仙教授现为J. Differential Equations、 Proc. Amer. Math. Soc.等杂志编委。在Memoirs of the American Mathematical Society、Transactions of the American Mathematical Society、SIAM 系列、Journal of Functional Analysis、Journal of Differential Equations等国际著名期刊上发表学术论文150余篇，并出版专著“Spectral Theory for random and nonautonomous parabolic equations and applications”。

内容介绍：This talk is concerned with front propagation dynamics in Fisher KPP equations on unbounded metric graphs. Such equations can be used to model the evolution of populations living in environments with network structure. There are several studies on front propagation phenomena in bistable equations on unbounded metric graphs. It is known that, in such equations, the network structure of the underlying environment may block the propagation of the fronts. It will be shown in this talk that the network structure of the environments does not block the propagation of the fronts in Fisher-KPP equations. In particular, it will be shown that the Fisher-KPP equation on an unbounded graph with finite many edges has the same spreading speed c? as the Fisher KPP equation on the real line R and has a generalized traveling wave connecting the stable positive constant solution and the trivial solution with averaged speed c for any c ＞ c?.