Stable viscosity matrices for systems of conservation laws

Andrew Majda, Robert L. Pego

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Feb 1985

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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