Special Session 12: Propagation Phenomena in Reaction-Diffusion Systems

Existence and stability of nontrivial solutions for bistable reaction-diffusion equations on graphs of finite length
Harunori Monobe
Osaka Metropolitan University
Japan
Co-Author(s):    Yoshihisa Morita
Abstract:
In this study, we consider the existence and stability of steady-state solutions to reaction-diffusion equations with a bistable nonlinearity on a graph of finite length. In this presentation, we first consider a ``star-graph`` consisting of a single junction and show the existence and stability of non-constant steady-state solutions when the edge lengths are sufficiently large. We then use these results to show the existence and stability of non-constant steady-state solutions on more complex graphs. This is a joint work with Professor Yoshihisa Morita.