Special Session 6: Propagation dynamics of PDEs: recent progress and trends

Front propagation dynamics in Fisher-KPP equations on unbounded metric graphs
Wenxian Shen
Auburn University
USA
Co-Author(s):    Hewan Shemtaga, Selim Sukhtaiev
Abstract:
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 phenomenon 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 $\mathbb{R}$ and has a generalized traveling wave connecting the stable positive constant solution and the trivial solution with averaged speed $c$ for any $c>c^*$.