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. © 2022 Wiley Periodicals LLC.

中文翻译：

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具有非单调反应函数的快速反应极限

我们分析了具有非单调反应函数和一个非扩散组分的反应扩散系统的快速反应极限。随着反应速度趋于无穷大，非扩散组分的浓度表现出快速振荡。我们准确地确定了它的 Young 度量，作为副产品，它证明了扩散分量的强收敛性，这一结果在先验估计中并不明显。我们的工作基于 Plotnikov 对前向-后向抛物线方程正则化的分析。我们根据动力学函数重写了他的想法，阐明了方法，带来了新的见解，放宽了对模型函数的假设，并为杨氏测度的演变提供了一个弱公式。© 2022 Wiley Periodicals LLC。