Hyperbolic systems of thermodynamically compatible conservation laws in continuum mechanics

The new class of hyperbolic systems of conservation laws is proposed. Every system belonging to this class is thermodynamically compatible, i.e., is generated by one thermodynamic potential alone and has an additional conservation law as a consequence. Besides, every system can be reduced to a symmetric hyperbolic form. Many well-known systems of continuum mechanics equations belong to a formulated class. Some new well-posed systems of conservation equations for complex media models are considered.