The Shock Solutions For Several Nonlinear Singularly Perturbed Problems

In this thesis, several singularly perturbed nonlinear boundary value problems with shock layer phenomena are mainly discussed. Under suitable conditions, ap-proximations of solutions for the problems are constructed by using Van Dyke's matching method and indirect matching method. And then for the first problem, the uniformly validity of the solution is proved by the theory of differential inequal-ities.The article is constructured as follows:In chapter 1, first of all, we sketch research significance and general situation of singularly perturbed problems and summarize achievements of singularly per-turbed problems (mainly shock layer problems) at home and abroad, then, we state preliminaries, main methods, main theories that we use and major works of this thesis.In the first section of chapter 2, we construct an approximation of the solution for the quasilinear problem by using Van Dyke's matching method. In the second section, the uniformly validity of the solution is proved by the theory of differential inequalities, and we give error estimation.In chapter 3, we discuss a class of high order nonlinear singularly perturbed two points boundary value problem where m,n (?) N+. An approximation of the solution for the problem is constructed by using the matching principle, and we point out that there is the multiplayer phenomenon for certain of k.In chapter 4, we consider a class of nonlinear singularly perturbed problem by indirect matching method, and also constuct the shock solution.