Development and application ofthe theory of reaction-diffusion system approximation

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