Geodesic
On solvability of stationary boundary value problem for the heat and mass transfer equations
Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 41-52.

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

The boundary-value problem for the stationary Boussinesq heat and mass transfer equations under inhomogeneous non-standard boundary conditions for the velocity and mixed boundary conditions for the temperature and concentration is investigated. The local existence and uniqueness theorems are proved. 
@article{DVMG_2004_5_1_a5,
     author = {A. B. Smishlyaev and D. A. Tereshko},
     title = {On solvability of stationary boundary value problem for the heat and mass transfer equations},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {41--52},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a5/}
}
TY  - JOUR
AU  - A. B. Smishlyaev
AU  - D. A. Tereshko
TI  - On solvability of stationary boundary value problem for the heat and mass transfer equations
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2004
SP  - 41
EP  - 52
VL  - 5
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a5/
LA  - ru
ID  - DVMG_2004_5_1_a5
ER  - 
%0 Journal Article
%A A. B. Smishlyaev
%A D. A. Tereshko
%T On solvability of stationary boundary value problem for the heat and mass transfer equations
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2004
%P 41-52
%V 5
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a5/
%G ru
%F DVMG_2004_5_1_a5
A. B. Smishlyaev; D. A. Tereshko. On solvability of stationary boundary value problem for the heat and mass transfer equations. Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 41-52. http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a5/

[1] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970, 288 pp. | MR

[2] R. Temam, Uravneniya Nave – Stoksa, Mir, M., 1981, 408 pp. | MR | Zbl

[3] V. Girault and P. A. Raviart, Finite element methods for Navier – Stokes equations, Theory and algorithms, Springer-Verlag, Berlin, 1986 | MR | Zbl

[4] A. V. Kazhikhov, “Razreshimost nekotorykh odnostoronnikh kraevykh zadach dlya uravnenii Nave – Stoksa”, Din. splosh. sredy, 1974, no. 16, 5–34, IG SO AN SSSR, Novosibirsk

[5] V. V. Ragulin, “K zadache o protekanii vyazkoi zhidkosti skvoz ogranichennuyu oblast pri zadannom perepade davleniya ili napora”, Din. splosh. sredy, 1976, no. 27, 78–92, IG SO AN SSSR, Novosibirsk | MR

[6] O. Pironneau, “Conditions aux limites sur la pression pour les équations de Stokes et de Navier – Stokes”, C. R. Acad. Sci. Série I, 303 (1986), 403–406 | MR | Zbl

[7] C. Bègue, C. Conca, F. Murat and O. Pironneau, “A nouveau sur les équations de Stokes et de Navier – Stokes avec des conditions aux limites sur la pression”, C. R. Acad. Sci. Série I, 304 (1987), 23–28 | MR

[8] C. Conca, F. Murat and O. Pironneau, “The Stokes and Navier-Stokes equations with boundary conditions involving the pressure”, Japan. J. Math., 20 (1994), 279–318 | MR | Zbl

[9] G. V. Alekseev, A. B. Smyshlyaev, D. A. Tereshko, Neodnorodnye kraevye zadachi dlya statsionarnykh uravnenii teplomassoperenosa, Preprint No 19 IPM DVO RAN, Dalnauka, Vladivostok, 2000

[10] G. V. Alekseev and D. A. Tereshko, “On solvability of inverse extremal problem for stationary equations of viscous heat conducting fluid”, J. Inverse Ill-Posed Probl., 6 (1998), 521–562 | DOI | MR | Zbl

[11] G. V. Alekseev, D. A. Tereshko, “Statsionarnye zadachi optimalnogo upravleniya dlya uravnenii gidrodinamiki vyazkoi teploprovodnoi zhidkosti”, Sib. zhurn. ind. mat., 1:2 (1998), 24–44 | MR | Zbl

[12] D. A. Tereshko, “Razreshimost ekstremalnoi zadachi dlya techeniya vyazkoi teploprovodnoi zhidkosti v kanale”, Dalnevost. mat. cb., 8, 1999, 130–139

[13] G. V. Alekseev, A. B. Smyshlyaev, Razreshimost neodnorodnykh kraevykh zadach dlya statsionarnykh uravnenii gidrodinamiki vyazkoi teploprovodnoi zhidkosti, Preprint No 6 IPM DVO RAN, Dalnauka, Vladivostok, 1999, 44 pp.

[14] G. V. Alekseev and A. B. Smishliaev, “Solvability of the boundary-value problems for the Boussinesq equations with inhomogeneous boundary conditions”, J. Math. Fluid Mech., 3:1 (2001), 18–39 | DOI | MR | Zbl

[15] G. V. Alekseev, “Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teplomassoperenosa”, DAN, 375:3 (2000), 315–319 | MR

[16] G. V. Alekseev, “Razreshimost obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii teplomassoperenosa”, Sib. mat. zhurn., 42:5 (2001), 971–991 | MR | Zbl

[17] D. A. Tereshko, “Kraevye zadachi teplomassoperenosa s odnorodnymi granichnymi usloviyami dlya skorosti”, Dalnevost. mat. zhurn., 3:1 (2002), 24–33

[18] G. V. Alekseev, A. B. Smyshlyaev, D. A. Tereshko, “Razreshimost kraevoi zadachi dlya statsionarnykh uravnenii teplomassoperenosa pri smeshannykh kraevykh usloviyakh”, Zhurn. vychisl. matem. i matem. fiz., 43:1 (2003), 66–80 | MR

[19] A. A. Illarionov, A. Yu. Chebotarev, Suschestvovanie slabykh reshenii smeshannoi statsionarnoi zadachi dlya uravnenii Nave – Stoksa, Preprint No 11 IPM DVO RAN, Dalnauka, Vladivostok, 1999

[20] A. A. Illarionov, A. Yu. Chebotarev, “O razreshimosti smeshannoi kraevoi zadachi dlya statsionarnykh uravnenii Nave – Stoksa”, Differ. uravn., 37:5 (2001), 689–695 | MR | Zbl

[21] A. A. Illarionov, “O razreshimosti kraevykh zadach dlya statsionarnykh uravnenii Nave – Stoksa”, Dalnevost. mat. zhurn., 2:1 (2001), 16–36

[22] G. V. Alekseev, R. V. Brizitskii, “Razreshimost obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii magnitnoi gidrodinamiki vyazkoi zhidkosti so smeshannymi granichnymi usloviyami”, Dalnevost. mat. zhurn., 4:1 (2003), 108–126