## Abstract

A natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension, u_{1} + f(u)_{x} = 0, uε{lunate}R^{m}, 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 u_{t} + f(u)_{x} = v(Du_{x})_{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 u_{1} + f′(u_{0}) u_{x} = vDu_{xx} should be well posed in L^{2} uniformly in v as v → 0. Previous examples of inadmissible viscosity matrices are accounted for through violation of the stability criterion.

Original language | English (US) |
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Pages (from-to) | 229-262 |

Number of pages | 34 |

Journal | Journal of Differential Equations |

Volume | 56 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1985 |

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics