论文标题
与非单极反应函数的快速反应极限
Fast reaction limit with nonmonotone reaction function
论文作者
论文摘要
我们分析了反应 - 扩散系统中具有非单极反应函数的快速反应极限和一个非扩散成分。由于反应速度趋向于无穷大，因此非扩散成分的浓度表现出快速振荡。我们确切地确定了其年轻度量，作为副产品，证明了扩散成分的强烈收敛性，这是从先验估计中不明显的结果。我们的工作是基于Plotnikov对前后抛物线方程的正则化分析。我们根据动力学功能改写了他的想法，该功能阐明了该方法，带来了新的见解，放松对模型功能的假设，并为年轻度量的演变提供了薄弱的表述。
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.
