On the nonlinear wave equation \(u_{tt}-B(t,\| u \|^2, \| u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\| u\|^2,\| u_x\|^2)\) associated with the mixed homogeneous conditions
type: Item
instance of: scholarly article
title: On the nonlinear wave equation \(u_{tt}-B(t,\| u \|^2, \| u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\| u\|^2,\| u_x\|^2)\) associated with the mixed homogeneous conditions
zbMATH Open document ID: 1072.35125
author: Nguyen Thanh Long
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-06-01T00:00:00Z
review text: An initial boundary value problem in a cylinder with mixed boundary conditions for the Kirchhoff type equation is considered. The author gives sufficient conditions under which the problem in question has a unique local weak solution. To obtain this result, a linear recurrent procedure and compactness arguments are exploited.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 2173097
zbMATH Keywords: Kirchhoff equation
zbMATH Keywords: existence
zbMATH Keywords: mixed boundary conditions
zbMATH Keywords: unique local weak solution
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.12.053
OpenAlex ID: W2015463651
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DOI: 10.1016/J.JMAA.2004.12.053
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description: scientific article; zbMATH DE number 2173097