Stable viscosities and shock profiles for systems of conservation laws

Author:
Robert L. Pego

Journal:
Trans. Amer. Math. Soc. **282** (1984), 749-763

MSC:
Primary 35L65; Secondary 35L67, 76L05

DOI:
https://doi.org/10.1090/S0002-9947-1984-0732117-1

MathSciNet review:
732117

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Abstract | References | Similar Articles | Additional Information

Abstract: Wide classes of high order "viscosity" terms are determined, for which small amplitude shock wave solutions of a nonlinear hyperbolic system of conservation laws are realized as limits of traveling wave solutions of a dissipative system . The set of such "admissible" viscosities includes those for which the dissipative system satisfies a linearized stability condition previously investigated in the case by A. Majda and the author. When we also establish admissibility criteria for singular viscosity matrices , and apply our results to the compressible Navier-Stokes equations with viscosity and heat conduction, determining minimal conditions on the equation of state which ensure the existence of the "shock layer" for weak shocks.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0732117-1

Keywords:
Shock profiles,
viscosity,
traveling waves,
center manifold,
compressible Navier-Stokes equations,
shock layer

Article copyright:
© Copyright 1984
American Mathematical Society