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1992•Journal of Shanghai Normal UniversityRequires access

Asymptotic Analysis for the Singularly Perturbed System of Integral Equations

In W

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Abstract

In this paper we consider the singular perturbation problem for the system of linear integral equations y(x)=∫_0~1K_11(x,s)y+(s)ds+∫_0~1K_(12)(x,s)z(s)ds+f(x,e),ez(x)=∫_0~1K_(21)(x,s)y(s)ds+∫_0~1K_(22)(x,s)z(s)ds+g(x,e).The existence and uniqueness of the solution are proved and the formal asymptotic expansion of the solution with two boundary layers is constructed by the method of boundary layer function. The expansion is uniformly valid and the estimation of remainder for the asymptotic solution is given.

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What this paper is about

In this paper we consider the singular perturbation problem for the system of linear integral equations y(x)=∫_0~1K_11(x,s)y+(s)ds+∫_0~1K_(12)(x,s)z(s)ds+f(x,e),ez(x)=∫_0~1K_(21)(x,s)y(s)ds+∫_0~1K_(22)(x,s)z(s)ds+g(x,e).The existence and uniqueness of the solution are proved and the formal asymptotic expansion of the solution with two boundary layers is constructed by the method of boundary layer function. The expansion is uniformly valid and the estimation of remainder for the asymptotic solution is given.

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Available abstract

In this paper we consider the singular perturbation problem for the system of linear integral equations y(x)=∫_0~1K_11(x,s)y+(s)ds+∫_0~1K_(12)(x,s)z(s)ds+f(x,e),ez(x)=∫_0~1K_(21)(x,s)y(s)ds+∫_0~1K_(22)(x,s)z(s)ds+g(x,e).The existence and uniqueness of the solution are proved and the formal asymptotic expansion of the solution with two boundary layers is constructed by the method of boundary layer function. The expansion is uniformly valid and the estimation of remainder for the asymptotic solution is given.

Key concepts: Remainder, Singular perturbation, Method of matched asymptotic expansions, Uniqueness, Asymptotic expansion, Mathematics, Mathematical analysis, Asymptotic analysis

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