Viscous limits for piecewise smooth solutions to systems of conservation laws

Jonathan Goodman, Zhouping Xin

Research output: Contribution to journalArticle

Abstract

In this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity. It is shown that if the solution of the problem with zero viscosity is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition, then there exist solutions to the corresponding system with viscosity that converge to the solutions of the system without viscosity away from shock discontinuities at a rate of order ε as the viscosity coefficient ε goes to zero. The proof uses a matched asymptotic analysis and an energy estimate related to the stability theory for viscous shock profiles.

Original languageEnglish (US)
Pages (from-to)235-265
Number of pages31
JournalArchive for Rational Mechanics and Analysis
Volume121
Issue number3
DOIs
StatePublished - Sep 1992

Fingerprint

Systems of Conservation Laws
Smooth Solution
Conservation
Viscosity
Shock
Zero
Matched Asymptotics
Entropy Condition
Asymptotic analysis
Energy Estimates
Stability Theory
Asymptotic Analysis
Dissipation
Discontinuity
Entropy
Converge
Coefficient

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Mathematics(all)
  • Mechanics of Materials
  • Computational Mechanics

Cite this

Viscous limits for piecewise smooth solutions to systems of conservation laws. / Goodman, Jonathan; Xin, Zhouping.

In: Archive for Rational Mechanics and Analysis, Vol. 121, No. 3, 09.1992, p. 235-265.

Research output: Contribution to journalArticle

Goodman, Jonathan ; Xin, Zhouping. / Viscous limits for piecewise smooth solutions to systems of conservation laws. In: Archive for Rational Mechanics and Analysis. 1992 ; Vol. 121, No. 3. pp. 235-265.
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