Global existence of strong solutions to a class of fully nonlinear wave equations with strongly damped terms
type: Item
instance of: scholarly article
title: Global existence of strong solutions to a class of fully nonlinear wave equations with strongly damped terms
zbMATH Open document ID: 1254.35050
DOI: 10.1155/2012/805158
author: Zhigang Pan
author: Hong Luo
author: Tian Ma
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: We consider the global existence of strong solutions for a class of fully nonlinear wave equations with strongly damping terms \(u_{tt} - k\Delta u_t = f(x, \Delta u) + g(x, u, Du, D^2u)\) in a bounded and smooth domain \(\Omega\) in \(\mathbb {R}^n\), where \(f(x, \Delta u)\) is a given monotone in \(\Delta u\) nonlinearity satisfying some dissipativity and growth restrictions, and \(g(x, u, Du, D^2 u)\) is in a sense subordinated to \(f(x, \Delta u)\). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution \(u \in L^\infty_{\text{loc}}((0, \infty), W^{2,p}(\Omega) \cap W^{1,p}_0(\Omega))\).
Mathematics Subject Classification ID: 35D35
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 6106315
zbMATH Keywords: spatial sequence technique
zbMATH Keywords: Galerkin approximation
Wikidata QID: Q58907384
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/805158
OpenAlex ID: W2102341398
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description: scientific article; zbMATH DE number 6106315