Quasi-averaging of the system of equations of one-dimensional motion of a viscous heat-conducting gas with rapidly oscillating data
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 38 (1998) no. 7, pp. 1204-1219 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_1998_38_7_a15,
     author = {A. A. Amosov and A. A. Zlotnik},
     title = {Quasi-averaging of the system of equations of one-dimensional motion of a viscous heat-conducting gas with rapidly oscillating data},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1204--1219},
     year = {1998},
     volume = {38},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_7_a15/}
}
TY  - JOUR
AU  - A. A. Amosov
AU  - A. A. Zlotnik
TI  - Quasi-averaging of the system of equations of one-dimensional motion of a viscous heat-conducting gas with rapidly oscillating data
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1998
SP  - 1204
EP  - 1219
VL  - 38
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_7_a15/
LA  - ru
ID  - ZVMMF_1998_38_7_a15
ER  - 
%0 Journal Article
%A A. A. Amosov
%A A. A. Zlotnik
%T Quasi-averaging of the system of equations of one-dimensional motion of a viscous heat-conducting gas with rapidly oscillating data
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1998
%P 1204-1219
%V 38
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_7_a15/
%G ru
%F ZVMMF_1998_38_7_a15
A. A. Amosov; A. A. Zlotnik. Quasi-averaging of the system of equations of one-dimensional motion of a viscous heat-conducting gas with rapidly oscillating data. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 38 (1998) no. 7, pp. 1204-1219. http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_7_a15/

[1] Bakhvalov N. S., Eglit M. E., “Protsessy v periodicheskikh sredakh, ne opisyvaemye v terminakh srednikh kharakteristik”, Dokl. AN SSSR, 268:4 (1983), 836–840 | MR | Zbl

[2] Bakhvalov N. S., Panasenko G. P., Osrednenie protsessov v periodicheskikh sredakh, Nauka, M., 1984 | Zbl

[3] Allaire G., “Homogenization and two-scale convergence”, SIAM J. Math. Analys., 23 (1992), 1482–1518 | DOI | MR | Zbl

[4] Serre D., “Variations de grande amplitude pour la densite d'un fluide visqueux compressible”, Physica. Ser. D, 48 (1991), 113–128 | DOI | Zbl

[5] Amosov A. A., Zlotnik A. A., “Razreshimost “v tselom” kvaziosrednennykh uravnenii odnomernogo dvizheniya vyazkoi barotropnoi sredy s negladkimi dannymi”, Vestn. MEI, 1994, no. 4, 7–24 | MR

[6] Amosov A. A., Zlotnik A. A., “Obosnovanie kvaziosrednennykh uravnenii odnomernogo dvizheniya vyazkoi barotropnoi sredy s bystro ostsilliruyuschimi svoistvami”, Dokl. RAN, 342:3 (1995), 295–299 | MR | Zbl

[7] Amosov A. A., Zlotnik A. A., “Edinstvennost i ustoichivost obobschennykh reshenii kvaziosrednennykh uravnenii odnomernogo dvizheniya vyazkoi barotropnoi sredy”, Differents. ur-niya, 31:7 (1995), 1123–1131 | MR | Zbl

[8] Amosov A. A., Zlotnik A. A., “O kvaziosrednennykh uravneniyakh odnomernogo dvizheniya vyazkoi barotropnoi sredy s bystroostsilliruyuschimi dannymi”, Zh. vychisl. matem. i matem. fiz., 36:2 (1996), 87–110 | MR | Zbl

[9] Amosov A. A., Zlotnik A. A., “Otsenka pogreshnosti kvaziosredneniya uravnenii dvizheniya vyazkoi barotropnoi sredy s bystroostsilliruyuschimi dannymi”, Zh. vychisl. matem. i matem. fiz., 36:10 (1996), 111–128 | MR | Zbl

[10] Amosov A. A., Titov D. A., Zlotnik A. A., “Finite difference scheme for the quasi-averaged equations of one-dimensional motion of a viscous barotropic medium”, Rus. J. Numer. Math. and Math. Modelling, 11:6 (1996), 445–475 | DOI | MR | Zbl

[11] Amosov A. A., Zlotnik A. A., “Svoistva “v tselom” kvaziosrednennykh uravnenii odnomernogo dvizheniya vyazkogo teploprovodnogo gaza”, Dokl. RAN, 346:2 (1996), 151–154 | MR | Zbl

[12] Amosov A. A., Zlotnik A. A., “Semidiscrete method for soving quasi-averaged equations of the one-dimensional motion of a viscous heat-conducting gas”, Rus. J. Numer. Math. and Math. Modelling, 12:3 (1997), 171–197 | DOI | MR | Zbl

[13] Amosov A. A., Zlotnik A. A., “Obosnovanie kvaziosredneniya uravnenii odnomernogo dvizheniya vyazkogo teploprovodnogo gaza s bystroostsilliruyuschimi svoistvami”, Dokl. RAN, 354:4 (1997), 439–442 | MR | Zbl

[14] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | Zbl

[15] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1976 | Zbl

[16] Iosida K., Funktsionalnyi analiz, Mir, M., 1967

[17] Gaevskii X., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978

[18] Kufner A., John O., Fučik S., Function spaces, Academia, Prague, 1977 | Zbl

[19] Sobolev S. L., Izbrannye voprosy teorii funktsionalnykh prostranstv i obobschennykh funktsii, Nauka, M., 1989

[20] Bensoussan A., Lions J. L., Papanicolaou G., Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978

[21] Oleinik O. A., Iosifyan G. A., Shamaev A. S., Matematicheskie zadachi teorii silno neodnorodnykh uprugikh sred, Izd-vo MGU, M., 1990

[22] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Fizmatgiz, M., 1993 | Zbl

[23] Valadier M., Admissible finctions and two-scale convergence, Prepubl., Départ. Math., Univ. Montpellier, France, 1995, 16 pp.

[24] Amosov A. A., “O slaboi skhodimosti odnogo klassa bystroostsilliruyuschikh funktsii”, Matem. zametki, 62:1 (1997), 145–150 | MR | Zbl

[25] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974

[26] Danford N., Shvarts Dzh., Lineinye operatory. Ch. I. Obschaya teoriya, Izd-vo inostr. lit., M., 1962

[27] Antontsev S. N., Kazhikhov A. V., Monakhov V. N., Kraevye zadachi mekhaniki neodnorodnykh zhidkostei, Nauka, Novosibirsk, 1983

[28] Amosov A. A., Zlotnik A. A., “Poludiskretnyi metod resheniya uravnenii odnomernogo dvizheniya neodnorodnogo vyazkogo teploprovodnogo gaza s negladkimi dannymi”, Izv. vuzov. Matematika, 1997, no. 4, 3–19 | MR | Zbl

[29] Zlotnik A. A., Amosov A. A., “Ob ustoichivosti obobschennykh reshenii uravnenii odnomernogo dvizheniya vyazkogo teploprovodnogo gaza”, Sibirskii matem. zh., 38:4 (1997), 767–789 | MR | Zbl

[30] Amosov A. A., Zlotnik A. A., “Zamechaniya o svoistvakh obobschennykh reshenii iz $V_2(Q)$ odnomernykh lineinykh parabolicheskikh zadach”, Vestn. MEI, 1996, no. 6, 15–29 | MR

[31] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976