New development in the theory of reaction-diffusion system approximation

我们处理了在大量重要的科学和工业环境中出现的非线性扩散问题。其难点在于扩散的非线性，问题在于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只包含简单反应和线性扩散的半线性反应-扩散系统的解。这表明非线性扩散的机理可以通过反应-扩散相互作用来捕捉。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揭示研究非线性问题的有效方法。

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.