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arXiv · 2302.00393

Self-Similar Pattern in Coupled Parabolic Systems as Non-Equilibrium Steady States

Alexander Mielke·Stefanie Schindler
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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.

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Alexander Mielke, Stefanie Schindler. 2023-02-01. Self-Similar Pattern in Coupled Parabolic Systems as Non-Equilibrium Steady States. https://arxiv.org/abs/2302.00393

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