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 r eplaces and simplifies greatly the concept of Young measures, avoiding the difficulties encountered when working in L-P. The general construction of t he two kinetic functions that,generate the entropies of 2 x 2 strictly hype rbolic 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 com pleted and specialized using the additional Galilean invariance. This allow s a full characterization of convex entropies. It yields a kinetic formulat ion consisting of two semi-kinetic equations which, as usual, are equivalen t to the infinite family of all the entropy inequalities.