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Generalized solutions of the Galilean invariant thermodynamically compatible conservation laws constructed using Godunov’s ideas. (English. Russian original) Zbl 1451.80016

Comput. Math. Math. Phys. 60, No. 4, 558-567 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 4, 567-577 (2020).
Summary: The Galilean invariant thermodynamically compatible conservation laws that admit a class of generalized solutions is analyzed. The main feature of the generalized solutions considered in this paper is that they describe smooth solutions with the kinetic energy and total pressure loss, which accompany the dynamic process of heat supply. The principal properties of the generalized solutions analyzed in Godunov’s works are the Galilean invariance and thermodynamic compatibilty of the original conservation laws under the closed mathematical formulation of the thermal gas-dynamic process.

MSC:

80A19 Diffusive and convective heat and mass transfer, heat flow
76N15 Gas dynamics (general theory)
35Q79 PDEs in connection with classical thermodynamics and heat transfer
35Q76 Einstein equations
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