Far Eastern Mathematical Journal

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On solvability of stationary boundary value problem for the heat and mass transfer equations


A. B. Smishlyaev, D. A. Tereshko

2004, issue 1, Ñ. 41–52


Abstract
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.

Keywords:
heat and mass transfer, existence and uniqueness theorems

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References

[1] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoj neszhimaemoj zhidkosti, Nauka, M., 1970, 288 s.
[2] R. Temam, Uravneniya Nav'e – Stoksa, Mir, M., 1981, 408 s.
[3] V. Girault and P. A. Raviart, Finite element methods for Navier – Stokes equations, Theory and algorithms, Springer-Verlag, Berlin, 1986.
[4] A. V. Kazhixov, “Razreshimost' nekotoryx odnostoronnix kraevyx zadach dlya uravnenij Nav'e – Stoksa”, Din. splosh. sredy, 1974, ¹ 16, 5–34, IG SO AN SSSR, Novosibirsk.
[5] V. V. Ragulin, “K zadache o protekanii vyazkoj zhidkosti skvoz' ogranichennuyu oblast' pri zadannom perepade davleniya ili napora”, Din. splosh. sredy, 1976, ¹ 27, 78–92, IG SO AN SSSR, Novosibirsk.
[6] O. Pironneau, “Conditions aux limites sur la pression pour les equations de Stokes et de Navier – Stokes”, C. R. Acad. Sci. Se?rie I, 303 (1986), 403–406.
[7] C. Be?gue, C. Conca, F. Murat and O. Pironneau, “A nouveau sur les e?quations de Stokes et de Navier – Stokes avec des conditions aux limites sur la pression”, C. R. Acad. Sci. Se?rie I, 304 (1987), 23–28.
[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.
[9] G. V. Alekseev, A. B. Smyshlyaev, D. A. Tereshko, Neodnorodnye kraevye zadachi dlya stacionarnyx uravnenij teplomassoperenosa, Preprint ¹ 19 IPM DVO RAN, Dal'nauka, 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.
[11] G. V. Alekseev, D. A. Tereshko, “Stacionarnye zadachi optimal'nogo upravleniya dlya uravnenij gidrodinamiki vyazkoj teploprovodnoj zhidkosti”, Sib. zhurn. ind. mat., 1:2 (1998), 24–44.
[12] D. A. Tereshko, “Razreshimost' e'kstremal'noj zadachi dlya techeniya vyazkoj teploprovodnoj zhidkosti v kanale”, Dal'nevost. mat. cb., 8, 1999, 130–139.
[13] G. V. Alekseev, A. B. Smyshlyaev, Razreshimost' neodnorodnyx kraevyx zadach dlya stacionarnyx uravnenij gidrodinamiki vyazkoj teploprovodnoj zhidkosti, Preprint ¹ 6 IPM DVO RAN, Dal'nauka, Vladivostok, 1999, 44 s.
[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.
[15] G. V. Alekseev, “Obratnye e'kstremal'nye zadachi dlya stacionarnyx uravnenij teplomassoperenosa”, DAN, 375:3 (2000), 315–319.
[16] G. V. Alekseev, “Razreshimost' obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij teplomassoperenosa”, Sib. mat. zhurn., 42:5 (2001), 971–991.
[17] D. A. Tereshko, “Kraevye zadachi teplomassoperenosa s odnorodnymi granichnymi usloviyami dlya skorosti”, Dal'nevost. mat. zhurn., 3:1 (2002), 24–33.
[18] G. V. Alekseev, A. B. Smyshlyaev, D. A. Tereshko, “Razreshimost' kraevoj zadachi dlya stacionarnyx uravnenij teplomassoperenosa pri smeshannyx kraevyx usloviyax”, Zhurn. vychisl. matem. i matem. fiz., 43:1 (2003), 66–80.
[19] A. A. Illarionov, A. Yu. Chebotarev, Sushhestvovanie slabyx reshenij smeshannoj stacionarnoj zadachi dlya uravnenij Nav'e – Stoksa, Preprint ¹ 11 IPM DVO RAN, Dal'nauka, Vladivostok, 1999.
[20] A. A. Illarionov, A. Yu. Chebotarev, “O razreshimosti smeshannoj kraevoj zadachi dlya stacionarnyx uravnenij Nav'e – Stoksa”, Differ. uravn., 37:5 (2001), 689–695.
[21] A. A. Illarionov, “O razreshimosti kraevyx zadach dlya stacionarnyx uravnenij Nav'e – Stoksa”, Dal'nevost. mat. zhurn., 2:1 (2001), 16–36.
[22] G. V. Alekseev, R. V. Brizickij, “Razreshimost' obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij magnitnoj gidrodinamiki vyazkoj zhidkosti so smeshannymi granichnymi usloviyami”, Dal'nevost. mat. Zhurn., 4:1 (2003), 108–126.

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