Research On The Classes Of Singularly Perturbed Reaction Diffusion Equation With Internal Layers

This dissertation aims to study the complication of Contrast Structures in two classes of singularly perturbed Reaction-diffusion problems.In recent years,due to the development of the theory of Contrast Structures,close attention has been paid to the problem with discontinuous term.In chapter one,the background,main theorems and definitions of singular perturbation theory,and the work and innovation of this paper has been described.In chapter two,a class of piecewise-continuous singularly perturbed reaction-diffusion problem has been studied.Formal asymptotic solution has been constructed and discussed by using boundary layer function method and qualitative analysis.A first-order continuous asymptotic solution has been constructed based on Contrast Structures and sewing method,the existence of solution has been proved,and the estimation of reminder has been given.In the third chapter,a class of non-linear singularly perturbed reaction-diffusion problem has been discussed.Formal asymptotic solution has been constructed by using boundary layer function method and local coordinate method.The existence of solution has been proved by Differential Inequality Method,and the estimation of reminder has been given.Besides,the problem with unfixed internal layer’s position with respect to time variable has been discussed,meanwhile,the type of problem has been changed from problem with internal layer to problem with boundary layer.