Geodesic
Nonisentropic one-dimensional gas motions constructed by means of the contact group of the nonhomogeneous Monge–Ampère equation
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 447-462 
S. V. Khabirov. Nonisentropic one-dimensional gas motions constructed by means of the contact group of the nonhomogeneous Monge–Ampère equation. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 447-462. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a11/
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     author = {S. V. Khabirov},
     title = {Nonisentropic one-dimensional gas motions constructed by means of the contact group of the nonhomogeneous {Monge{\textendash}Amp\`ere} equation},
     journal = {Sbornik. Mathematics},
     pages = {447--462},
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     volume = {71},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_2_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The equations of one-dimensional gas dynamics in Lagrange coordinates are connected with the inhomogeneous Monge–Ampère equation by means of a differential substitution. A classification of Monge–Ampère equations based on point and contact transformations is carried out. In the case of an infinite group various linearizations of the equations of gas dynamics are presented. New conservation laws are constructed on the basis of Nöther's theorem. Examples of invariant solutions with variable entropy are considered, and some boundary value problems with curved shock waves are also solved.

[1] Ovsyannikov L. V., Lektsii po osnovam gazovoi dinamiki, Nauka, M., 1981 | MR | Zbl

[2] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1968 | MR | Zbl

[3] Kurant G., Fridrikhs K., Sverkhzvukovoe techenie i udarnye volny, IL, M., 1950

[4] Sedov L. I., Metody podobiya i razmernosti v mekhanike, Nauka, M., 1965 | MR

[5] Korobeinikov V. P., Zadachi teorii tochechnogo vzryva, Nauka, M., 1985 | MR | Zbl

[6] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[7] Sheftel M. B., “O gruppakh Li-Beklunda, dopuskaemykh uravneniyami odnomernoi gazovoi dinamiki”, Vestn. LGU, 1982, no. 7, 37–41 | MR | Zbl

[8] Meshkov A. G., Mikhalyaev B. B., “Uravneniya gazovoi dinamiki, dopuskayuschie beskonechnoe chislo simmetrii”, TMF, 72:2 (1987), 163–171 | MR | Zbl

[9] Martin M. H., “The propagation of a plane shock into a quiet atmosphere”, Canad. J. Math., 3 (1953), 165–187 | MR | Zbl

[10] Zavyalov Yu. S., “O nekotorykh integralakh odnomernogo dvizheniya gaza”, DAN SSSR, 103:5 (1955), 781–782 | MR

[11] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR

[12] Lychagin V. V., Rubtsov V. N., “O teoremakh Sofusa Li dlya uravneniya Monzha-Ampera”, DAN BSSR, 27:5 (1983), 396–398 | MR | Zbl