Fast Reaction Limit with Nonmonotone Reaction Function

被引:3
|
作者
Perthame, Benoit [1 ]
Skrzeczkowski, Jakub [2 ]
机构
[1] Sorbonne Univ, Univ Paris, CNRS, INRIA,Lab Jacques Louis Lions, Paris, France
[2] Univ Warsaw, Fac Math Informat & Mech, Warsaw, Poland
基金
欧洲研究理事会;
关键词
REACTION-DIFFUSION SYSTEM; CROSS-DIFFUSION; PARABOLICITY; CONSERVATION; MODEL; BIFURCATION; PATTERNS; BEHAVIOR; EQUATION;
D O I
10.1002/cpa.22042
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We analyse the fast reaction limit in the reaction-diffusion system with nonmonotone reaction function and one nondiffusing component. As speed of reaction tends to infinity, the concentration of the nondiffusing 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 an 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. (c) 2022 Wiley Periodicals, Inc.
引用
收藏
页码:1495 / 1527
页数:33
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