Relaxation limit for piecewise smooth solutions to systems of conservation laws
type: Item
instance of: scholarly article
title: Relaxation limit for piecewise smooth solutions to systems of conservation laws
zbMATH Open document ID: 0949.35088
author: Wen-Qing Xu
published in: Journal of Differential Equations
publication date: 2000-11-26T00:00:00Z
review text: The author shows that any piecewise smooth solution \(u^0(x,t)\) of the equation \(u_t+f(u)_x=0\), \((x\in \mathbb{R}^n)\) with finitely many noninteracting shocks satisfying the entropy condition is a strong limit (as \(\varepsilon \rightarrow 0\)) of solutions \(u^{\varepsilon }(x,t)\) of the system \(u_t+v_x=0\), \(v_t+au_x=-{1\over \varepsilon }(v-f(u))\), \( u,v\in \mathbb{R}^n.\)
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 1437341
zbMATH Keywords: Cauchy problem
zbMATH Keywords: finitely many noninteracting shocks
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3653
OpenAlex ID: W1963644386
cites work: Zero relaxation and dissipation limits for hyperbolic conservation laws
cites work: Hyperbolic conservation laws with stiff relaxation terms and entropy
cites work: The relaxation schemes for systems of conservation laws in arbitrary space dimensions
cites work: Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation
cites work: Viscous limits for piecewise smooth solutions to systems of conservation laws
cites work: Hyperbolic conservation laws with relaxation
cites work: Q4892756
cites work: Asymptotic limit of initial boundary value problems for conservation laws with relaxational extensions
cites work: The fluid-dynamic limit of the Broadwell model of the nonlinear Boltzmann equation in the presence of shocks
cites work: Stiff well-posedness and asymptotic convergence for a class of linear relaxation systems in a quarter plane
DOI: 10.1006/JDEQ.1999.3653
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description: scientific article; zbMATH DE number 1437341