Mappings of domains connected with the Dirichlet problem for the equation of vibrating string
type: Item
instance of: scholarly article
title: Mappings of domains connected with the Dirichlet problem for the equation of vibrating string
zbMATH Open document ID: 0818.35068
published in: Journal of Mathematics of Kyoto University
publication date: 1994-12-19T00:00:00Z
review text: This paper is concerned with the solvability of the Dirichlet problem for the vibrating string equation \(u_{xx} - u_{yy} + f(x,y,u) = 0\), \((x,y) \in \Omega\) with \(u |_{\partial \Omega} = 0\), in which \(\Omega\) is a bounded domain with piecewise smooth boundaries. The problem is re-written in a simpler form of a type first noticed by Fritz John, and the result is used to establish existence, uniquenesss and regularity for weak solutions under certain conditions. The main objective of the paper is to derive necessary and sufficient conditions for the functions used when mapping the problem into one involving the simpler form.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 701490
zbMATH Keywords: Dirichlet problem for the vibrating string equation
zbMATH Keywords: existence, uniquenesss and regularity for weak solutions
author: Andrei A. Lyashenko
reviewed by: Alan Jeffrey
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519014
OpenAlex ID: W1508287931
DOI: 10.1215/KJM/1250519014
Recommended article: Q3218514
Recommended article: The solvability of the Dirichlet problem for the vibrating string equation in domains with corner points
Recommended article: Q3252846
Recommended article: Q3507991
Recommended article: On the Dirichlet problem for the nonlinear equation of the vibrating string. I
Recommended article: The Dirichlet problem for the semilinear vibrating string equation in a class of domains with corner points
Recommended article: On the Dirichlet problem for the nonlinear equation of the vibrating string. II
Recommended article: Normal solvability of the Dirichlet problem for the vibrating string equation in domains with nonsmooth boundaries
Recommended article: Riemann-Hilbert problems for the system of string vibration equations in a domain with a characteristic part of boundary
description: scientific article; zbMATH DE number 701490