Stable spikes for a reaction-diffusion system with two activators and one inhibitor

Speaker: Matthias Winter

Date: 2021

Location: UBC, Vancouver, Canada, Online

Conference: PIMS Workshop on New Trends in Localized Patterns in PDES

Subject: Mathematics

Class: Scientific

Abstract:

We consider a reaction-diffusion system with two activators and one inhibitor. We prove rigorous results on the existence and stability of spiky patterns. We show that for certain conditions on the parameters these solutions can be stable. The approach is based on analytical methods such as elliptic estimates, Liapunov-Schmidt reduction and nonlocal eigenvalue problems. This is joint work with Weiwei Ao and Juncheng Wei.