## Abstract

For scalar conservation laws, the kinetic formulation makes it possible to generate all the entropies from a simple kernel. We show how this concept replaces and simplifies greatly the concept of Young measures, avoiding the difficulties encountered when working in L^{p}. The general construction of the two kinetic functions that generate the entropies of 2 × 2 strictly hyperbolic systems is also developed here. We show that it amounts to building a "universal" entropy, i.e., one that can be truncated by a "kinetic value" along Riemann invariants. For elastodynamics, this construction can be completed and specialized using the additional Galilean invariance. This allows a full characterization of convex entropies. It yields a kinetic formulation consisting of two semi-kinetic equations which, as usual, are equivalent to the infinite family of all the entropy inequalities.

Original language | English (US) |
---|---|

Pages (from-to) | 1-48 |

Number of pages | 48 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 155 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2000 |

## ASJC Scopus subject areas

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering