主講人：Wenxian Shen，Professor at Auburn University

時(shí)間：2025年5月28日9:30

地點(diǎn)：徐匯校區(qū)三號(hào)樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：沈文仙教授為國(guó)際知名微分方程動(dòng)力系統(tǒng)專(zhuān)家，多年來(lái)致力于研究微分方程中的動(dòng)力學(xué)問(wèn)題，包括異質(zhì)和隨機(jī)介質(zhì)理論中的行波解，單調(diào)動(dòng)力系統(tǒng)中的Lyapunov指數(shù)理論，非局部擴(kuò)散算子的譜理論及應(yīng)用，擬周期反應(yīng)擴(kuò)散方程的漸近動(dòng)力學(xué)行為，特別是與其合作者所發(fā)展的非自治單調(diào)斜積半流理論已成為處理許多非自治方程動(dòng)力系統(tǒng)的重要工具。沈文仙教授現(xiàn)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(guó)際著名期刊上發(fā)表學(xué)術(shù)論文150余篇，并出版專(zhuān)著“Spectral Theory for random and nonautonomous parabolic equations and applications”。

內(nèi)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?.