Stephan, Artur
(2021)
*EDP-convergence for a linear reaction-diffusion system with
fast reversible reaction.*
Calculus of Variations, 60
(226).
pp. 1-35.

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610kB |

Official URL: https://doi.org/10.1007/s00526-021-02089-0

## Abstract

We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction.We understand the linear reaction-diffusion system as a gradient flow of the free energy in the space of probability measures equipped with a geometric structure, which contains the Wasserstein metric for the diffusion part and cosh-type functions for the reaction part. The fast-reaction limit is done on the level of the gradient structure by proving EDP-convergence with tilting. The limit gradient system induces a diffusion system with Lagrange multipliers on the linear slow-manifold.Moreover, the limit gradient system can be equivalently described by a coarse-grained gradient system, which induces a diffusion equation with a mixed diffusion constant for the coarse-grained slow variable.

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: | 2677 |

Deposited By: | Monika Drueck |

Deposited On: | 24 Jan 2022 15:30 |

Last Modified: | 24 Jan 2022 15:30 |

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