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The shock structure in a binary mixture of polyatomic Eulerian gases withdifferent degrees of freedom of a molecule is studied based on themulti-temperature model of rational extended thermodynamics. Since the systemof field equations is hyperbolic, the shock-structure solution is not alwaysregular, and discontinuous parts (sub-shocks) can be formed. For given valuesof the mass ratio and the specific heats of the constituents, we identify thepossible sub-shocks as the Mach number $M_0$ of the shock wave and theconcentration $c$ of the constituents change. In the plane $(c,M_0)$, weidentify the possible regions for the sub-shock formation. The analysis isobtained to verify when the velocity of the shock wave meets a characteristicvelocity in the unperturbed or perturbed equilibrium states that gives anecessary condition for the sub-shock formation. The condition becomesnecessary and sufficient when the velocity of the shock becomes greater thanthe maximum characteristic velocity in the unperturbed state. Namely, theregions with no sub-shocks, a sub-shock for only one constituent, or sub-shocksfor both constituents are comprehensively classified. The most interesting caseis that the lighter molecule has more degrees of freedom than that of the heavyone. In this situation, the topology of the various regions becomes different.We also solve the system of the field equations numerically using theparameters in the various regions and confirm whether the sub-shocks emerge ornot. Finally, the relationship between an acceleration wave in a constituentand the sub-shock in the other constituent is explicitly derived.

A Complete Classification of Sub-Shocks in the Shock Structure of a Binary Mixture of Eulerian Gases with Different Degrees of Freedom