On the existence and absence of global solutions of the first Darboux problem for nonlinear wave equations
type: Item
instance of: scholarly article
title: On the existence and absence of global solutions of the first Darboux problem for nonlinear wave equations
zbMATH Open document ID: 1156.35431
DOI: 10.1134/S0012266108030087
author: G. K. Berikelashvili
author: O. Jokhadze
author: B. Midodashvili
author: S. Kharibegashvili
published in: Differential Equations
publication date: 2008-09-22T00:00:00Z
review text: The first Darboux problem to the equation \(u_{tt}-u_{xx}+\lambda u\left| u\right| ^{\alpha }=f(x,t)\) is considered. Existence of a global strong generalized solution of the problem for either \(-1<\alpha<0\) or \(\alpha ,\lambda >0\) is proved. In the case of \(\lambda <0,\alpha >0\) the problem has no global strong generalized solution, but under some assumptions on \(f(x,t)\) local solution exists.
reviewed by: Marie Kopáčková
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35R25
zbMATH DE Number: 5345622
zbMATH Keywords: strong generalized solution
MaRDI profile type: Publication
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full work available at URL: s0012266108030087
OpenAlex ID: W2061622346
description: scientific article; zbMATH DE number 5345622