On hyperbolic systems with entropy velocity covariant under the action of a group

Abstract

For hyperbolic systems of conservation laws in one space dimension endowed with a mathematical entropy, we define the notion of entropy velocity and we give sufficient conditions for such a system to be covariant under the action of a group of space-time transformations. These conditions naturally introduce a representation of the group in the space of states. We construct such hyperbolic systems from the knowledge of data on the manifold of null velocity. We apply these ideas for Galileo, Lorentz, and circular groups and, in particular, focus on nontrivial examples of [Formula: see text] systems of conservation laws.