Global solvability of the Cauchy characteristic problem for one class of nonlinear second order hyperbolic systems
type: Item
instance of: scholarly article
title: Global solvability of the Cauchy characteristic problem for one class of nonlinear second order hyperbolic systems
zbMATH Open document ID: 1213.35296
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-02-09T00:00:00Z
review text: The solution of the system \(\frac{\partial ^2}{\partial t^2}u_{i}-\Delta u_{i}+\lambda \frac{\partial }{\partial u_{i}}G(u_1, u_2,\dots u_{N})=F_{i}(x,t)\), \(i=1,2,\dots N\) in \(\{[x,t]\in \mathbb {R}^{n+1}\: | x| <t<T\}\) satisfying the conditions \(u_{i}(x,| x| )=0,\) where \(n,N\geq 2\) is discussed. Under certain assumptions on the function \(G\) the authors prove existence and uniqueness of the strong generalized solution of the problem.
reviewed by: Marie Kopáčková
Mathematics Subject Classification ID: 35L52
Mathematics Subject Classification ID: 35L71
zbMATH DE Number: 5848918
zbMATH Keywords: strong generalized solution
author: S. Kharibegashvili
author: B. Midodashvili
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.10.056
OpenAlex ID: W1988296142
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DOI: 10.1016/J.JMAA.2010.10.056
description: scientific article; zbMATH DE number 5848918