Hyperbolicity of first and second order extended thermodynamics theory of polyatomic rarefied gases

The balance laws of Rational Extended Thermodynamics describe well the evolution of rarefied gases in non-equilibrium. Usually, it is necessary to approximate the theory in a neighborhood of an equilibrium state andconsequently, its hyperbolicity property remains valid only in a neighborhood of the equilibrium state of thefield variables, calledhyperbolicityregion. The goal of this paper is first to determine the differential system with14 fields for a rarefied polyatomic polytropic gas, approximated at the second-order in the non-equilibriumvariables. Then, we investigate and compare the hyperbolicity property of the first-order and second-ordersystems. In particular, we analyze the role played by the dynamic pressure and the molecular degrees offreedom. Finally, we also show that in the monatomic singular limit the quadratic theory for a polyatomic gasconverges to the corresponding quadratic theory for a monatomic gas.