Kinetic formulation for systems of two conservation laws and elastodynamics

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.