Kinetic formulation for systems of two conservation laws and elastodynamics

Benoit Perthame*, Athanasios Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

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 Lp. 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 languageEnglish (US)
Pages (from-to)1-48
Number of pages48
JournalArchive for Rational Mechanics and Analysis
Volume155
Issue number1
DOIs
StatePublished - Jan 1 2000

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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