STRUCTURAL ANALYSIS OF SOLUTIONS TO SINGULARLY PERTURBED EQUATIONS IN COMPLEX DOMAINS.

Abstract

This paper presents a structural analysis of solutions to singularly perturbed equations in complex domains. The need for such an approach is explained by the fact that the asymptotic behavior of solutions to singularly perturbed equations in different parts of the considered complex domains is different. This paper is devoted to solving this problem for SPE systems consisting of two first-order equations. The solution to the problem consists of two parts. The first part presents some geometric constructions that serve as a basis for further research. The second part, according to the geometric constructions, presents a study of the asymptotic behavior of solutions to the problem.

For structural analysis, the solution to the problem under consideration is split into three components. One of them is the solution to the unperturbed equation, the second characterizes the boundary layer lines and domains, and the third is the attraction domain.