Double-periodic boundary value problem for nonlinear dissipative hyperbolic equations
type: Item
instance of: scholarly article
title: Double-periodic boundary value problem for nonlinear dissipative hyperbolic equations
zbMATH Open document ID: 0717.35057
DOI: 10.1016/0022-247X(90)90426-G
author: Wan Se Kim
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The author considers the existence of the weak solution of the double- periodic problem for nonlinear dissipative hyperbolic equations of the form \[ \beta u_ t+u_{tt}-u_{xx}-g(t,x,u)=h(t,x)\text{ in } \Omega =[0,2\pi]\times [0,2\pi], \] with \(\beta\neq 0\), \(h\in L^ 2(\Omega)\), and g: \(\Omega\times {\mathbb{R}}\to {\mathbb{R}}\) is a Carathéodory function. In the last years several papers dealt with this problem for various types of the nonlinear term g. By use of an abstract continuation theorem of \textit{J. Mawhin} [Topological degree methods in nonlinear boundary value problems, Reg. Conf. Ser. Math. No.40, Am. Math. Soc. (1979; Zbl 0414.34025)] the author succeeds in weakening some conditions on g.
reviewed by: Karl Heinz Jansen
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 4181912
zbMATH Keywords: double-periodic
zbMATH Keywords: nonlinear dissipative hyperbolic equations
MaRDI profile type: Publication
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description: scientific article