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

2023/02/01 by Alexander Mielke, Mielke, Alexander, Schindler, Stefanie
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Hydrocarbon exploration and reservoir analysis #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2302.00393

openalex publication_date 2023/02/01 · openalex created_date 2023/02/04 · openalex updated_date 2026/08/01

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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