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We analyze a mathematical model for the relaxation of translational and internal temperatures in a nonequilibrium gas. The system of partial differential equations-derived from the kinetic theory of gases-is recast in its natural entropic symmetric form as well as in a convenient hyperbolic-parabolic symmetric form. We investigate the Chapman-Enskog expansion in the fast relaxation limit and establish that the temperature difference becomes asymptotically proportional to the divergence of thedoi:10.3934/krm.2015.8.79 fatcat:tcqouownubewpkc3qqhuwcfixe