Abstract
The compatibility between balance laws and the entropy principle implies that any hyperbolic system becomes a Godunov symmetric system if we choose as variables the main field. The consequence is the well-posedness of Cauchy problem. Rational Extended Thermodynamics (RET) is a theory for nonequilibrium gases that belongs in this mathematical framework and is motivated at the mesoscopic scale by the kinetic theory. We present in this contribution some recent results and some open problems on RET for both monatomic and polyatomic gases.
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