New development in the 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。在本研究中，我们证明了非线性扩散问题的解可以近似为半线性反应扩散方程组的解，其中只包括简单反应和线性扩散。这表明，非线性扩散机制可能是由反应扩散相互作用捕获。解决半线性问题通常比处理非线性问题更容易。因此，反应扩散系统近似理论有望为非线性问题的研究提供有效的途径。

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 proved that the solutions of the nonlinear diffusion problems can be approximated by those of semilinear reaction-diffusion systems which include only simple reactions and linear diffusions. This indicates that the mechanism of nonlinear diffusion might be captured by reaction-diffusion interaction. Resolving semilinear problems is typically easier than dealing with nonlinear problems. Therefore, the theory of reaction-diffusion system approximation is expected to reveal effective approaches to the study of nonlinear problems.