Stable discontinuous stationary solutions to certain reaction-diffusion systems
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with the no-flux boundary condition will be presented in a context of pattern formation. Such initial boundary value problems may have different types of stationary solutions. Regular (i.e. sufficiently smooth) stationary solutions exist, however, all of them are unstable. The goal of this talk is to explain how to construct discontinuous stationary solutions to general reaction-diffusion-ODE systems and to show their stability.
This is a joint work with Szymon Cygan, Anna Marciniak-Czochra, and Kanako Suzuki.