Almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small BV initial data
type: Item
instance of: scholarly article
title: Almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small BV initial data
zbMATH Open document ID: 1272.35150
author: Zhi-Qiang Shao
published in: Journal of Differential Equations
publication date: 2013-03-20T00:00:00Z
review text: The author considers the Riemann solutions to a strictly hyperbolic and genuinely nonlinear system of conservation laws, which consist only of shock waves. The structural stability of these solutions under \(C^1\)-smooth perturbations of the Riemann data is studied. The author obtains the almost global existence and lifespan of piecewise \(C^1\)-smooth solutions of the perturbed problem. Applications to the system of one-dimensional isentropic flow are also given.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 6147006
zbMATH Keywords: genuinely nonlinear characteristic fields
zbMATH Keywords: generalized Riemann problem
zbMATH Keywords: piecewise \(C^1\)-smooth solutions
zbMATH Keywords: shock waves
reviewed by: Evgeniy Panov
MaRDI profile type: Publication
full work available at URL: j.jde.2013.01.004
OpenAlex ID: W1989617010
DOI: 10.1016/J.JDE.2013.01.004
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description: scientific article; zbMATH DE number 6147006