主講人：Wenxian Shen，Professor at Auburn University

時間：2025年5月28日9:30

地點：徐匯校區三號樓332室

舉辦單位：數理學院

主講人介紹：沈文仙教授為國際知名微分方程動力系統專家，多年來致力于研究微分方程中的動力學問題，包括異質和隨機介質理論中的行波解，單調動力系統中的Lyapunov指數理論，非局部擴散算子的譜理論及應用，擬周期反應擴散方程的漸近動力學行為，特別是與其合作者所發展的非自治單調斜積半流理論已成為處理許多非自治方程動力系統的重要工具。沈文仙教授現為J. Differential Equations、 Proc. Amer. Math. Soc.等雜志編委。在Memoirs of the American Mathematical Society、Transactions of the American Mathematical Society、SIAM 系列、Journal of Functional Analysis、Journal of Differential Equations等國際著名期刊上發表學術論文150余篇，并出版專著“Spectral Theory for random and nonautonomous parabolic equations and applications”。

內容介紹：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?.