Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898814 | Journal of Differential Equations | 2018 | 41 Pages |
Abstract
In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fixed point argument around a numerically computed solution, in the spirit of the Newton-Kantorovich theorem. It allows to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we obtain as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Maxime Breden, Roberto Castelli,