Interior Layer Phenomena In Nonlinear Singular Perturbation Problems

In this dissertation, some nonlinear singular perturbation problems with interior layer are mainly discussed. The article is structured as follows:The first chapter provides a brief introduction to the historical development and some application background of singular perturbation.The second chapter presents some preliminary concept and results which will be required later.The third chapter consists of two parts.In section 1 we considerA formal approximation of the problem is constructed using the method of composite expansisons, and then the existence of the shock layer solution is proved by Harten fixed point theorem. In section 2 we considerε2x"+t2n+1x'+g(t,x)=0, a<t<b x(a,ε)=A, x(b,ε)=B.A formal approximation of the problem is constructed using the method of composite expansisons, and then the existence of the spike layer solution is proved by the theory of differential inequalities.The fourth chapter considers Under the principal assumption that t=0 is a turning piont for the functions f and g, solutions are shown to exhibit one of two types of nonmonotone interior layer beharior:spike layer behavior or nonmonotone transition layer behavior.Using the mothed of constructing component-wise upper and lower solutions and the theory of differential inequalities,the existence of solutions are proved and the asymptotic estimates of solutions are given.