English

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}
}