Global existence of classical solutions to the Cauchy problem for a kind of quasilinear hyperbolic systems in divergence form
type: Item
instance of: scholarly article
title: Global existence of classical solutions to the Cauchy problem for a kind of quasilinear hyperbolic systems in divergence form
zbMATH Open document ID: 1178.35240
author: Yan Guan
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-08-20T00:00:00Z
review text: The authors consider the global existence of classical solution to a kind of second order quasilinear hyperbolic system subject to a null condition, with the linear elastodynamic system as its principal part and the nonlinear terms in divergence form depending on the product of \(u^2\) and the derivatives of \(u\). Basing on the fact that the nonlinear terms are of divergence form they obtained the generalized energy estimate for nonlocal energy. Using the generalized energy estimate they showed the global existence of classical solutions the considered Cauchy problem for small initial data.
Mathematics Subject Classification ID: 35L51
Mathematics Subject Classification ID: 35L72
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74H40
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 5597533
zbMATH Keywords: null condition
zbMATH Keywords: linear elastodynamic system
zbMATH Keywords: generalized energy estimate
zbMATH Keywords: small initial data
reviewed by: Jerzy August Gawinecki
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.05.050
OpenAlex ID: W2012041756
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DOI: 10.1016/J.JMAA.2009.05.050
description: scientific article; zbMATH DE number 5597533