Mielke, A. and Mittnenzweig, M.
(2018)
*Convergence to Equilibrium in Energy-Reaction–Diffusion Systems Using Vector-Valued Functional Inequalities.*
Journal of Nonlinear Science
.
pp. 1-42.
ISSN 1432-1467 (online)

Full text not available from this repository.

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 |
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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: | 18 Mar 2022 10:02 |

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