The Pure Boundary Layer And Step-type Contrast Structure Of Two-dimension Singular Perturbation System

In this paper, we mainly study two-dimension singular perturbation system with boundary values of the first type, and we respectively discuss the two cases in which this problem have pure boundary layer and step-type contrast structure.In chapter 1, we simply introduce some basic conception of singular perturbation and the work that has been done, and list the main idea of this paper.In chapter 2, we discuss the above two-dimension singular perturbation system with boundary values of the first type which only has pure boundary layer, we construct the asymptotic solution of the problem by boundary layer function method under the hypotheses and prove that all boundary layer terms decay exponentially , then we construct the upper and lower solutions based on the formal asymptotic solution, and prove the existence of the problem and estimate the remainder terms by means of differential inequality.In chapter 3, we discuss the problem with step-type contrast structure, we show the hypotheses under which this problem has step-type contrast structure, and divide the problem into right and left problems with boundary values, then we use boundary layer function method to construct the asymptotic solution and prove the existence of the solution.In chapter 4, we extend the foregoing problems forward, we discuss the possibility that the problem can be extended to high dimension, render the readers to think about and work it out.