Repository: Freie Universität Berlin, Math Department

Convergence to Equilibrium in Energy-Reaction–Diffusion Systems Using Vector-Valued Functional Inequalities

Mielke, A. and Mittnenzweig, M. (2017) Convergence to Equilibrium in Energy-Reaction–Diffusion Systems Using Vector-Valued Functional Inequalities. Journal of Nonlinear Science . pp. 1-42. ISSN 1432-1467 (online)

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Official URL: https://dx.doi.org/10.1007/s00332-017-9427-9

Abstract

We discuss how the recently developed energy dissipation methods for reaction diffusion systems can be generalized to the non-isothermal case. For this, we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions, we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2153
Deposited By: Silvia Hoemke
Deposited On:07 Dec 2017 18:16
Last Modified:07 Dec 2017 18:16

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