Stable viscosity matrices for systems of conservation laws

Andrew Majda, Robert L. Pego

Research output: Contribution to journalArticle

Abstract

A natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension, u1 + f(u)x = 0, uε{lunate}Rm, is studied. These matrices are admissible in the sense that small-amplitude shock wave solutions of the hyperbolic system are shown to be limits of smooth traveling wave solutions of the parabolic system ut + f(u)x = v(Dux)x as ifv → 0 if D is in this class. The class is determined by a linearized stability requirement: The Cauchy problem for the equation u1 + f′(u0) ux = vDuxx should be well posed in L2 uniformly in v as v → 0. Previous examples of inadmissible viscosity matrices are accounted for through violation of the stability criterion.

Original languageEnglish (US)
Pages (from-to)229-262
Number of pages34
JournalJournal of Differential Equations
Volume56
Issue number2
DOIs
StatePublished - 1985

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Systems of Conservation Laws
Conservation
Viscosity
Stability criteria
Shock waves
Hyperbolic Systems of Conservation Laws
Parabolic Systems
Hyperbolic Systems
Traveling Wave Solutions
Stability Criteria
Shock Waves
Cauchy Problem
Strictly
Requirements
Class

ASJC Scopus subject areas

  • Analysis

Cite this

Stable viscosity matrices for systems of conservation laws. / Majda, Andrew; Pego, Robert L.

In: Journal of Differential Equations, Vol. 56, No. 2, 1985, p. 229-262.

Research output: Contribution to journalArticle

Majda, Andrew ; Pego, Robert L. / Stable viscosity matrices for systems of conservation laws. In: Journal of Differential Equations. 1985 ; Vol. 56, No. 2. pp. 229-262.
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