Decay to equilibrium for energy-reaction-diffusion systems
| Autor: | Alexander Mielke, Peter Markowich, Sabine Hittmeir, Jan Haskovec |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
entropy entropy-production balance
log-Sobolev inequality Type (model theory) 01 natural sciences Mathematics - Analysis of PDEs Convergence (routing) Reaction–diffusion system FOS: Mathematics 0101 mathematics Mathematics Internal energy Applied Mathematics Principle of maximum entropy 35B40 010102 general mathematics Mathematical analysis 35K57 35B40 35Q79 010101 applied mathematics Computational Mathematics 35K57 Heat equation dissipation functional entropy functional Balanced flow Energy-reaction-diffusion systems 35Q79 Analysis Energy (signal processing) Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1602.05696 |
| Popis: | We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitely calculable constants and establish the convergence to thermodynamical equilibrium, at first in entropy and further in $L^1$ using Cziszar-Kullback-Pinsker type inequalities. Comment: 40 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|