Speaker: Hewan Shemtaga (Auburn University)
Title: Fisher-KPP Equations and Chemotaxis Models on Metric Graphs
Abstract: In this talk, I will first provide an overview of the research projects I have been working on, including the global existence and long-time dynamics of chemotaxis models on compact as well as unbounded metric graphs. The focus will then shift to my recent work with Dr. Wenxian Shen and Dr. Selim Sukhtaiev on front propagation dynamics in Fisher-KPP equations on unbounded metric graphs. Specifically, we introduce a notion of generalized traveling wave solutions on unbounded star graphs for the first time and establish their existence for all speeds c > c∗ = 2√a. Moreover, we show that on any unbounded metric graph with finitely many edges, the Fisher-KPP equation admits the same minimal spreading speed c∗ = 2√a as on the real line.