Convergence to equilibrium in energy-reaction–diffusion systems using vector-valued functional inequalities

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Item Type:	Article
Title:	Convergence to equilibrium in energy-reaction–diffusion systems using vector-valued functional inequalities
Creators Name:	Mielke, A. and Mittnenzweig, M.
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.
Keywords:	Energy-Reaction-Diffusion Systems, Vector-Valued Inequalities, Cross Diffusion, log-Sobolev Inequality, Entropy Functional, Exponential Decay of Relative Entropy, Convexity Method
Source:	Journal of Nonlinear Science
ISSN:	0938-8974
Publisher:	Springer
Volume:	28
Number:	2
Page Range:	765-806
Date:	April 2018
Official Publication:	https://doi.org/10.1007/s00332-017-9427-9

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