勷勤数学•杰出学者报告

题      目：Front propagation on a general metric graph

报  告  人：Hiroshi Matano 教授  (邀请人：丁维维)

                                      日本明治大学

时      间： 12月10日  15：00-16:00

地     点：数科院西楼111报告厅

报告人简介:

       Hiroshi Matano (俣野博)教授，国际著名数学家，日本东京大学名誉教授、明治大学特任教授，研究领域是非线性分析和非线性偏微分方程。1990年获得日本数学界最高奖—春季奖，1994年受邀参加国际数学家大会（ICM，苏黎世）并应邀做45分钟报告。2003年-2004年担任日本数理经济学会会长，2018-2023年担任明治大学先端数理科学研究所所长，曾担任多个国际一流学术杂志的编委。Matano教授是国际公认的非线性抛物方程领域的领军专家，在很多方面做出过里程碑式的贡献，这些研究工作包括：他是单调动力系统理论的奠基人之一；他给出的零点性质已成为研究抛物方程定性理论的有力工具；他将行波解概念推广到递归情形；在爆破问题、渐近行为中的应用及非线性分析的多个方面也有开创性的研究成果。

摘      要：

        We consider a bistable reaction-diffusion equation on a metric graph that consists of a general bounded finite metric graph $D$, which we call the "center graph", and a finite number of "outer paths" that stretch from $D$ toward infinity. Our goal is to investigate the behavior of solution fronts that come from infinity along a given outer path and to discuss whether or not the front can propagate into other outer paths. For that purpose, we introduce the notion of "propagation" and "blocking".

       We first focus on general principles that hold regardless of the structure of $D$, such as the dichotmy and transient principles. Next we consider perturbations of the graph $D$ while fixing the outer paths, and discuss whether or not the propagation and blocking properties are preserved under perturbations. We also consider several specific classes of graphs, such as those with a "reservoir" type subgraph, and study their intriguing properties.

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