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 and consequently, its hyperbolicity property remains valid only in a neighborhood of the equilibrium state of the field variables, called hyperbolicity region. The goal of this paper is first to determine the differential system with 14 fields for a rarefied polyatomic polytropic gas, approximated at the second-order in the non-equilibrium variables. Then, we investigate and compare the hyperbolicity property of the first-order and second-order systems. In particular, we analyze the role played by the dynamic pressure and the molecular degrees of freedom. Finally, we also show that in the monatomic singular limit the quadratic theory for a polyatomic gas converges to the corresponding quadratic theory for a monatomic gas.