Stable discontinuous stationary solutions to reaction-diffusion-ODE systems
Analysis of PDEs
2023-04-14 v2
Abstract
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial boundary value problems may have different types of stationary solutions. In our parallel work [Instability of all regular stationary solutions to reaction-diffusion-ODE systems (2021)], regular (i.e. sufficiently smooth) stationary solutions are shown to exist, however, all of them are unstable. The goal of this work is to construct discontinuous stationary solutions to general reaction-diffusion-ODE systems and to find sufficient conditions for their stability.
Cite
@article{arxiv.2111.01214,
title = {Stable discontinuous stationary solutions to reaction-diffusion-ODE systems},
author = {Szymon Cygan and Grzegorz Karch and Anna Marciniak-Czochra and Kanako Suzuki},
journal= {arXiv preprint arXiv:2111.01214},
year = {2023}
}
Comments
31 pages, 3 figures