A two-point problem for systems of hyperbolic equations
type: Item
instance of: scholarly article
title: A two-point problem for systems of hyperbolic equations
zbMATH Open document ID: 0732.35044
DOI: 10.1007/BF01060820
author: L. B. Urmancheva
author: Yu. A. Mitropol'skij
published in: Ukrainian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The work deals with a two-dimensional nonlinear hyperbolic system of the form \[ (1)\quad \partial^ 2u/\partial t\partial x=P(t,x)u(t,x)+f(t,x,u,u_ t), \] where \(x\in [-a,a]\), \(t\in [0,T]\). The initial and boundary conditions for (1) are given by \[ (2)\quad u(0,x)=u_ 0(0)+v(x),\quad Au(0,x)+Cu(T,x)=w(x),\quad u(t,0)=u_ 0(t)+v(0). \] Here \(u,v,u_ 0,w,f\) are vector-valued functions, while P,A,C are matrices. Assuming f is Lipschitz continuous and the matrices P,A,C satisfy suitable assumptions, the authors prove the existence of a solution and construct an approximation sequence of functions tending to the solution. An estimate of the error of the approximation sequence is also established.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35L50
zbMATH DE Number: 4210655
zbMATH Keywords: two-dimensional nonlinear hyperbolic
zbMATH Keywords: existence
zbMATH Keywords: approximation sequence
reviewed by: Vladimir Georgiev
MaRDI profile type: Publication
cites work: Numerical-Analytic Methods in the Theory of Boundary-Value Problems
cites work: Q3220952
description: scientific article; zbMATH DE number 4210655