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

François Dubois (1, 2)

1 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés
2 LMO - Laboratoire de Mathématiques d'Orsay

For hyperbolic systems of conservation laws in one space dimension with a mathematical entropy, we define the notion of entropy velocity. Then 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 system from the knowledge of data on the manifold of null velocity. We apply these ideas for Galileo, Lorentz and circular groups. We focus on particular non trivial examples for two by two systems of conservation laws.

Mots clés: mathematical entropy; circular group; Lorentz group; Galileo group

Domaines: Equations aux dérivées partielles [math.AP]

François Dubois. On hyperbolic systems with entropy velocity covariant under the action of a group. Journal of Hyperbolic Differential Equations, 2015, 12 (04), pp.763-785. ⟨10.1142/s0219891615500228⟩. ⟨hal-00860736v2⟩