Geodesic
Symmetries and solutions to equations of two-dimensional motions of polytropic gas
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 291-307 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The optimal system of subalgebras for the $9$-dimensional Lie algebra was constructed. This system classifies invariant submodels of equation governing the motion of polytropic gas with polytrope-exponent $\gamma=2$. Invariant submodels of rank equal to 0 were found and their physical properties were described. 
@article{SEMR_2005_2_a20,
     author = {A. S. Pavlenko},
     title = {Symmetries and solutions to equations of two-dimensional motions of polytropic gas},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {291--307},
     year = {2005},
     volume = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a20/}
}
TY  - JOUR
AU  - A. S. Pavlenko
TI  - Symmetries and solutions to equations of two-dimensional motions of polytropic gas
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2005
SP  - 291
EP  - 307
VL  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2005_2_a20/
LA  - ru
ID  - SEMR_2005_2_a20
ER  - 
%0 Journal Article
%A A. S. Pavlenko
%T Symmetries and solutions to equations of two-dimensional motions of polytropic gas
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2005
%P 291-307
%V 2
%U http://geodesic.mathdoc.fr/item/SEMR_2005_2_a20/
%G ru
%F SEMR_2005_2_a20
A. S. Pavlenko. Symmetries and solutions to equations of two-dimensional motions of polytropic gas. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 291-307. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a20/

[1] Ovsyannikov L. V., “Programma PODMODELI. Gazovaya dinamika”, PMM, 58:4 (1994), 30–55 | MR | Zbl

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

[3] Golovin S. V., Optimalnaya sistema podalgebr dlya algebry Li operatorov, dopuskaemykh uravneniyami gazovoi dinamiki v sluchae politropnogo gaza, Preprint, In-t gidrodinamiki SO RAN, Novosibirsk, 1996, 5–96

[4] Cherevko A. A., Optimalnaya sistema podalgebr dlya algebry Li operatorov, dopuskaemykh sistemoi uravnenii gazovoi dinamiki s uravneniem sostoyaniya $p=f(S)\rho^{5/3}$, Preprint, In-t gidrodinamiki SO RAN, Novosibirsk, 1996, 4–96

[5] Ovsyannikov L. V., Lektsii po osnovam gazovoi dinamiki, In-t kompyuternykh issledovanii, M., Izhevsk, 2003

[6] Golovin S. V., “Two-dimensional gas motion with special symmetry properties”, Proceeding of the International Conference MGA 2000 (Ufa 27.09–03.10 2000), 71–76

[7] Ibragimov N. H., CRC Handbook of Lie Group Analysis of Differential Equations, v. 1, Symmetries, Exact Solutions and Conservation Laws, CRC Press, Boca Raton, 1994 | MR | Zbl

[8] Ovsyannikov L. V., “Ob ierarkhii invariantnykh podmodelei differentsialnykh uravnenii”, Dokl. RAN, 8:6 (1998), 740–742 | MR

[9] Ovsyannikov L. V., “Ob optimalnykh sistemakh podalgebr”, Dokl. RAN, 333:6 (1993), 702–704 | MR | Zbl

[10] Ovsyannikov L. V., “O “prostykh” resheniyakh uravnenii dinamiki politropnogo gaza”, PMTF, 40:2 (1999) | Zbl

[11] Chupakhin A. P., Barokhronnye dvizheniya gaza: obschie svoistva i podmodeli tipov (1,2) i (1,1), Preprint, In-t gidrodinamiki SO RAN, Novosibirsk, 1998, 4–98