Global existence and asymptotic behavior of classical solutions of quasilinear hyperbolic systems with linearly degenerate characteristic fields
type: Item
instance of: scholarly article
title: Global existence and asymptotic behavior of classical solutions of quasilinear hyperbolic systems with linearly degenerate characteristic fields
zbMATH Open document ID: 1129.35047
author: Wen-Rong Dai
author: De-Xing Kong
published in: Journal of Differential Equations
publication date: 2007-04-19T00:00:00Z
review text: The authors study the global existence and the asymptotic behavior of classical solutions of the Cauchy problem for quasilinear hyperbolic system \(\partial_t u +A(u)\partial_x u=0\) under the assumption that it is hyperbolic with constant multiple characteristic fields. They prove that the global \(C^1\)-solution exists uniquely if the BV-norm of the initial datum is sufficiently small. Moreover, when time \(t\) tends to infinity, this solution approaches a combination of \(C^1\)-traveling wave solutions.
reviewed by: Grzegorz Karch
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 5144845
zbMATH Keywords: large time asymptotics
zbMATH Keywords: traveling wave solutions
zbMATH Keywords: normalized coordinates
zbMATH Keywords: constant multiple characteristic fields
MaRDI profile type: Publication
full work available at URL: j.jde.2006.12.020
OpenAlex ID: W1994578052
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DOI: 10.1016/J.JDE.2006.12.020
description: scientific article; zbMATH DE number 5144845