Mielke, Alexander and Mittnenzweig, Markus
(2018)
*Convergence to Equilibrium in
Energy-Reaction–Diffusion Systems Using
Vector-Valued Functional Inequalities.*
Journal of Nonlinear Science, 28
.
pp. 765-806.
ISSN 1432-1467 (online)

PDF
577kB |

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

## Abstract

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 > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2665 |

Deposited By: | Monika Drueck |

Deposited On: | 17 Jan 2022 17:13 |

Last Modified: | 17 Jan 2022 17:13 |

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