Asymptotics of the solutions to singularly perturbed multidimensional integral equations
type: Item
instance of: scholarly article
title: Asymptotics of the solutions to singularly perturbed multidimensional integral equations
zbMATH Open document ID: 0824.45001
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-06-08T00:00:00Z
review text: The object of the study in the paper is the singularly perturbed integral equation of the form \[ \varepsilon h_ \varepsilon(x)+ \int_ T R(x- y) h_ \varepsilon(y) dy= f(x),\tag{1} \] \(x\in T\), where \(\varepsilon> 0\) is a parameter, \(T\) is a bounded domain in \(\mathbb{R}^ n\) with a smooth boundary and \(f(x)\) is a given smooth function. Moreover, \(R(x)= P(D) G(x)\), where \(P(D)\) is a differential operator and \(G(x)\) is a fundamental solution. Extending some methods developed earlier an asymptotic solution of the equation (1) is constructed. The estimate of the error of that solution is given. Some examples of application are also provided.
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 762181
zbMATH Keywords: multidimensional integral equations
zbMATH Keywords: singular perturbation
zbMATH Keywords: error estimate
zbMATH Keywords: asymptotic solution
author: A. G. Ramm
author: Efim I. Shifrin
reviewed by: Józef Banaś
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1102
OpenAlex ID: W2033520885
DOI: 10.1006/JMAA.1995.1102
description: scientific article; zbMATH DE number 762181