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Monatomic rarefied gas as a singular limit of polyatomic gas in extended thermodynamics. (English) Zbl 1297.76143

Summary: We show that, in the theory of extended thermodynamics, rarefied monatomic gases can be identified as a singular limit of rarefied polyatomic gases. Under naturally conditioned initial data we prove that the system of 14 field equations for polyatomic gases in the limit has the same solutions as those of the system of 13 field equations for monatomic gases where there exists no dynamic pressure. We study two illustrative examples in the process of the limit, that is, the linear waves and the shock waves in order to grasp the asymptotic behavior of the physical quantities, in particular, of the dynamic pressure.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35Q35 PDEs in connection with fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
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