| 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 $c>c^*$. |
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