Geodesic
Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 325-337 
A. A. Zlotnik. Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 325-337. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a11/
@article{ZVMMF_2010_50_2_a11,
     author = {A. A. Zlotnik},
     title = {Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {325--337},
     year = {2010},
     volume = {50},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a11/}
}
TY  - JOUR
AU  - A. A. Zlotnik
TI  - Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 325
EP  - 337
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a11/
LA  - ru
ID  - ZVMMF_2010_50_2_a11
ER  - 
%0 Journal Article
%A A. A. Zlotnik
%T Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 325-337
%V 50
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a11/
%G ru
%F ZVMMF_2010_50_2_a11

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

Energy equalities are derived for the barotropic quasi-gasdynamic, modified quasi-gasdynamic, and quasi-hydrodynamic systems of equations. Global energy estimates of solutions are obtained. For the second of the systems, necessary and sufficient conditions for nonuniform and uniform Petrovskii parabolicity are derived.

[1] Chetverushkin B. N., Kineticheskie skhemy i kvazigazodinamicheskaya sistema uravnenii, MAKS Press, M., 2004; Chetverushkin B. N., Kinetic schemes and quasi-gas dynamics system of equations, CIMNE, Barcelona, 2008

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

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

[4] Elizarova T. G., Sokolova M. E., Sheretov Yu. V., “Kvazigazodinamicheskie uravneniya i chislennoe modelirovanie techenii vyazkogo gaza”, Zh. vychisl. matem. i matem. fiz., 45:3 (2005), 545–556 | MR | Zbl

[5] 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

[6] Zlotnik A. A., “O parabolichnosti kvazigidrodinamicheskoi sistemy uravnenii i ustoichivosti malykh vozmuschenii dlya nee”, Matem. zametki, 83:5 (2008), 667–682 | MR | Zbl

[7] Zlotnik A. A., “O nekotorykh svoistvakh uravnenii dvumernoi kvazigazodinamicheskoi modeli transportnykh potokov”, Zh. vychisl. matem. i matem. fiz., 49:2 (2009), 373–381 | MR | Zbl

[8] Petrovskii I. G., Izbrannye trudy. Sistemy uravnenii s chastnymi proizvodnymi. Algebraicheskaya geometriya, Nauka, M., 1986 | MR

[9] Eidelman S. D., Parabolicheskie sistemy, Nauka, M., 1964 | MR