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Article Dans Une Revue Communications on Pure and Applied Mathematics Année : 2022

Fast reaction limit with nonmonotone reaction function

Résumé

We analyse fast reaction limit in the reaction-diffusion system with nonmonotone reaction function and one non-diffusing component. As speed of reaction tends to infinity, the concentration of non-diffusing component exhibits fast oscillations. We identify precisely its Young measure which, as a by-product, proves strong convergence of the diffusing component, a result that is not obvious from a priori estimates. Our work is based on analysis of regularization for forward-backward parabolic equations by Plotnikov. We rewrite his ideas in terms of kinetic functions which clarifies the method, brings new insights, relaxes assumptions on model functions and provides a weak formulation for the evolution of the Young measure.

Dates et versions

hal-02922284 , version 1 (26-08-2020)

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Benoît Perthame, Jakub Skrzeczkowski. Fast reaction limit with nonmonotone reaction function. Communications on Pure and Applied Mathematics, 2022, ⟨10.1002/cpa.22042⟩. ⟨hal-02922284⟩
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