Development and application ofthe theory of reaction-diffusion system approximation

我们处理了大量重要的科学和工业背景下产生的非线性扩散问题。困难来自于扩散的非线性，问题是如何处理扩散的非线性。本文主要研究反应扩散方程组逼近理论，其中非线性扩散方程组的解被半线性反应扩散方程组的解逼近。我们在快反应极限问题的分析、反应扩散方程组近似的分析及其在数值分析和数学建模中的应用方面取得了一些成果

We dealt with nonlinear diffusion problems arising in a large number of important scientific and industrial contexts. The difficulties arise from the nonlinearity of the diffusion and the problem is how to handle the nonlinearity of the diffusion. In this study, we focused on the theory of reaction-diffusion system approximation in which the solutions of the nonlinear diffusion problems are approximated by those of semilinear reaction-diffusion systems. We achieved several results regarding analysis of Fast reaction limit problems, analysis of reaction-diffusion system approximation and its applications to numerical analysis and mathematical modeling