Repository: Freie Universit├Ąt Berlin, Math Department

EDP-convergence for a linear reaction-diffusion system with fast reversible reaction

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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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
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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