Asymptotic behaviour at infinity of solutions of multidimensional second kind integral equations
type: Item
instance of: scholarly article
title: Asymptotic behaviour at infinity of solutions of multidimensional second kind integral equations
zbMATH Open document ID: 0845.45004
author: A. T. Peplow
author: Simon N. Chandler-Wilde
published in: Journal of Integral Equations and Applications
publication date: 1996-08-20T00:00:00Z
review text: This is the continuation of the two earlier works of the first author [ibid. 4, No. 2, 153-177 (1992; Zbl 0756.45004)]. Let \(\Omega \subset \mathbb{R}^n\) be an unbounded open set and let \(X\) be the space of bounded and continuous functions on \(\overline \Omega\). For \(p \geq 0\), let \(W_p (s) = (1 + |s |)^p\) and let \(X_p\) denote the weighted space \(X_p : = \{x \in X : |x |^p_\infty : = |w_p x |_\infty < \infty\}\). In the space \(X_p\), the integral equation \[ x(s) - \int_\Omega k (s,t) x(t)dt = y(s),\;s \in \overline \Omega \] is considered. An application to acoustics is given.
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 76Q05
zbMATH DE Number: 851874
zbMATH Keywords: asymptotic behaviour at infinity
zbMATH Keywords: multidimensional second kind integral equations
reviewed by: Zbigniew Binderman
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075881
OpenAlex ID: W2091429212
cites work: Q3694636
cites work: Numerical solutions of integral equations on the half line. I: The compact case
cites work: The Numerical Solution of Integral Equations on the Half-Line
cites work: A general look at local principles with special emphasis on the norm computation aspect
cites work: Q4040771
cites work: On the behaviour at infinity of solutions of integral equations on the real line
cites work: On asymptotic behavior at infinity and the finite section method for integral equations on the half-line
cites work: Q3272062
cites work: Ground effect analysis: Surface wave and layer potential representations
cites work: Q3050932
cites work: The field of a spherical wave reflected from a plane absorbent surface expressed in terms of an infinite series of Legendre polynomials
cites work: OPERATORS OF CONVOLUTION TYPE IN CONES
cites work: Q3715553
cites work: Reflection of waves from a point source by an impedance boundary
DOI: 10.1216/JIEA/1181075881
description: scientific article; zbMATH DE number 851874