Fast reaction limit with nonmonotone reaction function
Analysis of PDEs
2021-12-03 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2008.11086,
title = {Fast reaction limit with nonmonotone reaction function},
author = {Benoît Perthame and Jakub Skrzeczkowski},
journal= {arXiv preprint arXiv:2008.11086},
year = {2021}
}