Geodesic
On the quasi-gasdynamic system of equations with general equations of state and a~heat source
Matematičeskoe modelirovanie, Tome 22 (2010) no. 7, pp. 53-64.

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The quasi-gasdynamic system of equations with a mass force and a heat source is well known in the case of the perfect polytropic gas. In the paper, the system is generalized for the case of general equations of gas state satisfying thermodynamic stability conditions. The entropy balance equation is studied. The validity of the non-negativity property is algebraically analyzed for the entropy production. Two different forms of notation are derived for its relaxation summands. Under a condition on the heat source intensity, the property is valid.
Mots-clés : quasi-gasdynamic system of equations
Keywords: general equations of gas state, heat source, entropy balance equation. 
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A. A. Zlotnik. On the quasi-gasdynamic system of equations with general equations of state and a~heat source. Matematičeskoe modelirovanie, Tome 22 (2010) no. 7, pp. 53-64. http://geodesic.mathdoc.fr/item/MM_2010_22_7_a3/

[1] Chetverushkin B. N., Kineticheskie skhemy i kvazigazodinamicheskaya sistema uravnenii, MAKS Press, M., 2004

[2] Elizarova T. G., Kvazigazodinamicheskie uravneniya i metody rascheta vyazkikh techenii, Nauchnyi mir, M., 2007

[3] Sheretov Yu. V., Dinamika sploshnykh sred pri prostranstvenno-vremennom osrednenii, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva–Izhevsk, 2009

[4] Chetverushkin B. N., Matematicheskoe modelirovanie zadach dinamiki izluchayuschego gaza, Nauka, M., 1985 | Zbl

[5] Zlotnik A. A., “Klassifikatsiya nekotorykh modifikatsii sistemy uravnenii Eilera”, Dokl. RAN, 407:6 (2006), 747–751 | MR

[6] Zlotnik A. A., Chetverushkin B. N., “O parabolichnosti kvazigazodinamicheskoi sistemy uravnenii, ee giperbolicheskoi 2-go poryadka modifikatsii i ustoichivosti malykh vozmuschenii dlya nikh”, Zh. vychisl. matem. i matem. fiz., 48:3 (2008), 445–472 | MR | Zbl

[7] Zlotnik A. A., “Energeticheskie ravenstva i otsenki dlya barotropnykh kvazigazo- i kvazigidro- dinamicheskikh sistem uravnenii”, Zh. vychisl. matem. i matem. fiz., 50:2 (2010), 325–337

[8] Elizarova T. G., Quasi-gas dynamic equations, Springer, Berlin-Heidelberg, 2009 | Zbl

[9] Zlotnik A. A., “Kvazigazodinamicheskaya sistema uravnenii s obschimi uravneniyami sostoyaniya”, Dokl. RAN, 431:5 (2010), 605–609 | MR

[10] Kvasnikov I. A., Termodinamika i statisticheskaya fizika, v. 1, Teoriya ravnovesnykh sistem. Termodinamika, Izd. 2-e, Editorial URSS, M., 2002

[11] Gantmakher F. R., Teoriya matrits, Nauka, M., 1988 | MR | Zbl