WIAS Preprint No. 2992, (2023)
Self-similar pattern in coupled parabolic systems as non-equilibrium steady states
- Mielke, Alexander
- Schindler, Stefanie
2020 Mathematics Subject Classification
- 35C06 35K40 35K57 35K65 80M30
- Coupled parabolic systems, reaction-diffusion systems, scaling laws, self-similarity, non-equilibrium steady states
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.