Nonlinear finite-part singular integral equations arising in two-dimensional fluid mechanics
type: Item
instance of: scholarly article
title: Nonlinear finite-part singular integral equations arising in two-dimensional fluid mechanics
zbMATH Open document ID: 0963.45008
DOI: 10.1016/S0362-546X(98)00347-2
author: E. G. Ladopoulos
author: V. A. Zisis
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-06-17T00:00:00Z
review text: The authors study a nonlinear Volterra integral equation of the type \[ u(x) = F\{x,u(x)\Phi(u),B_1(u),\ldots,B_k(u)\} + v(x), \] where \(\Phi\) is a finite-part integral \[ \Phi(u) = {1 \over 2\pi i} \int_L {u(t) \over (t-x)^\mu} \] (here \(\mu\) is a positive integer and \(L\) a contour) and \(B_j(u) = \int_L K_j(x,t)u(t) dt\). First an approximation method is used to prove the existence of a solution, and then the same approximation method is studied further with the purpose of getting numerical approximations of the solution. The paper ends with an application to a two-dimensional fluid mechanics problem.
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 1491652
zbMATH Keywords: nonlinear finite-part singular integral equations
zbMATH Keywords: nonlinear Volterra integral equation
zbMATH Keywords: approximation method
zbMATH Keywords: two-dimensional fluid mechanics
reviewed by: Olof Staffans
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00347-2
OpenAlex ID: W2059101746
Wikidata QID: Q128011670
description: scientific article; zbMATH DE number 1491652