Mielke, Alexander and Peletier, Mark A. and Stephan, Artur
(2021)
*EDP-convergence for nonlinear fast–slow reaction systems with detailed balance.*
Nonlinearity, 34
(8).
pp. 5762-5798.

Full text not available from this repository.

Official URL: https://doi.org/10.1088/1361-6544/ac0a8a

## Abstract

We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows. In general, the effective entropy will no longer be of Boltzmann type and the reactions will no longer satisfy mass-action kinetics.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

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

ID Code: | 3174 |

Deposited By: | Lukas-Maximilian Jaeger |

Deposited On: | 05 Sep 2024 08:51 |

Last Modified: | 05 Sep 2024 08:51 |

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