Stable viscosity matrices for systems of conservation laws

123Citations
Citations of this article
13Readers
Mendeley users who have this article in their library.

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. © 1985.

Cite

CITATION STYLE

APA

Majda, A., & Pego, R. L. (1985). Stable viscosity matrices for systems of conservation laws. Journal of Differential Equations, 56(2), 229–262. https://doi.org/10.1016/0022-0396(85)90107-X

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free