Self-Similar Pattern in Coupled Parabolic Systems as Non-Equilibrium Steady States
Analysis of PDEs
2023-02-02 v1
Abstract
We consider reaction-diffusion systems and other related dissipative systems on unbounded domains which would have a Liapunov function (and gradient structure) when posed on a finite domain. In this situation, the system may reach local equilibrium on a rather fast time scale but the infinite amount of mass or energy leads to persistent mass or energy flow for all times. In suitably rescaled variables the system converges to a steady state that corresponds to asymptotically self-similar behavior in the original system.
Keywords
Cite
@article{arxiv.2302.00393,
title = {Self-Similar Pattern in Coupled Parabolic Systems as Non-Equilibrium Steady States},
author = {Alexander Mielke and Stefanie Schindler},
journal= {arXiv preprint arXiv:2302.00393},
year = {2023}
}