On nonlinear theory dynamics of dilute gas
Matematičeskoe modelirovanie, Tome 16 (2004) no. 1, pp. 67-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

In framework of BGK (Bhatnagar, Gross and Kruck) model the boundary-value problem for nonlinear integro-differential Boltzmann equation is considered. By means of corresponding transformations, the problem is reduced to «weak» connected quazilinear system of integral equations. Such normal form of Boltzmann equation allow us to analyse statement of boundary-value problem and to suggest effective methods for it solution. As example, the results for two classic problems of kinetic theory of gases are applied.
@article{MM_2004_16_1_a4,
     author = {N. B. Engibaryan and A. Kh. Khachatryan},
     title = {On nonlinear theory dynamics of dilute gas},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {67--74},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_1_a4/}
}
TY  - JOUR
AU  - N. B. Engibaryan
AU  - A. Kh. Khachatryan
TI  - On nonlinear theory dynamics of dilute gas
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 67
EP  - 74
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_1_a4/
LA  - ru
ID  - MM_2004_16_1_a4
ER  - 
%0 Journal Article
%A N. B. Engibaryan
%A A. Kh. Khachatryan
%T On nonlinear theory dynamics of dilute gas
%J Matematičeskoe modelirovanie
%D 2004
%P 67-74
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2004_16_1_a4/
%G ru
%F MM_2004_16_1_a4
N. B. Engibaryan; A. Kh. Khachatryan. On nonlinear theory dynamics of dilute gas. Matematičeskoe modelirovanie, Tome 16 (2004) no. 1, pp. 67-74. http://geodesic.mathdoc.fr/item/MM_2004_16_1_a4/

[1] Bogolyubov N. N., Problemy dinamicheskoi teorii statisticheskoi fiziki, M., L., 1946 | MR

[2] Chempen S, Kauling P., Matematicheskaya teoriya neodnorodnykh gazov, M., 1960

[3] Karleman T., Matematicheskie zadachi kineticheskoi teorii gazov, M., 1960

[4] Kogan M. N., Dinamika razrezhennogo gaza, Nauka, M., 1962, 440 pp.

[5] Cherchinyani K., Teoriya i prilozheniya uravneniya Boltsmana, Mir, M., 1978, 495 pp. | MR

[6] Siewert C. E., J. Comput. Phys., 152 (1999), 251 | DOI | MR | Zbl

[7] Barichello L. B. and Siewert C. E., European Journal of Applied Matlematics, 2000, 314 pp.

[8] Latyshev A. V., TMF, 86:3 (1991), 402 | MR

[9] Bhatnagar P. L., Gross E. P. and Krook M., Phys. Rev., 94 (1954), 511 | DOI | Zbl

[10] Ambartsumyan V. A., Teoriya zvezdnykh spektrov, Nauka, M., 1966, 91 pp.

[11] Engibaryan N. B., Astrofizika, 1:3 (1965), 297

[12] Engibaryan N. B., Khachatryan A. Kh., Astrofizika, 23:1 (1985), 145 | MR

[13] Engibaryan N. B., Khachatryan A. Kh., TMF, 125:2 (2000), 339 | MR | Zbl

[14] Engibaryan N. B., Khachatryan A. Kh., ZhVM i MF, 38:3 (1998), 466–482 | MR | Zbl

[15] Korolyuk B. C., Brodi S. M., Turbin A. F., Itogi nauki. Teoriya veroyatnostei. Mat. statistika. Teoriya kibernetika, 11, VINITI AN SSSR, M., 1974, 47–97