On the nonlinear wave equation \(u_{tt}-B(\|u_{x} {\|}^{2})u_{xx}\) = \(f(x,t,u,u_{x},u_{t},{\|}u_{x}{\|}^{2})\) associated with the mixed homogeneous conditions
type: Item
instance of: scholarly article
title: On the nonlinear wave equation \(u_{tt}-B(\|u_{x} {\|}^{2})u_{xx}\) = \(f(x,t,u,u_{x},u_{t},{\|}u_{x}{\|}^{2})\) associated with the mixed homogeneous conditions
zbMATH Open document ID: 1028.35091
author: Nguyen Thanh Long
author: Bui Tien Dung
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-11-10T00:00:00Z
review text: Using Galerkin method the authors prove the existence and uniqueness of the weak solution to the nonlinear wave equation \(u_{tt}-B(\|u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\|u_x\|^2)\) on \((0,1)\times (0,T)\) satisfying homogeneous mixed boundary conditions and some small initial data. Small perturbations of \(f\) are also discussed.
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 2001957
zbMATH Keywords: one space dimension
zbMATH Keywords: Galerkin method
zbMATH Keywords: nonlocal terms
zbMATH Keywords: asymptotic expansion
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: j.na.2003.07.002
OpenAlex ID: W1991328363
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DOI: 10.1016/J.NA.2003.07.002
description: scientific article; zbMATH DE number 2001957