A complete classification of sub-shocks in the shock structure of a binary mixture of Eulerian gases with different degrees of freedom

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