Discontinuous stationary solutions to certain reaction-diffusion systems
Analysis of PDEs
2022-07-01 v1
Abstract
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the Brusselator model, the Gray-Scott model, the Oregonator model and a certain predator-prey model. It is shown that the considered systems have the both smooth and discontinuous stationary solutions, however, only discontinuous ones can be stable.
Cite
@article{arxiv.2206.15161,
title = {Discontinuous stationary solutions to certain reaction-diffusion systems},
author = {Szymon Cygan and Anna Marciniak-Czochra and Grzegorz Karch},
journal= {arXiv preprint arXiv:2206.15161},
year = {2022}
}
Comments
14 pages, 3 figures