The solvability of a boundary value problem for time-independent equations of heat and mass transfer under mixed boundary conditions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 66-80 Cet article a éte moissonné depuis la source Math-Net.Ru

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G. V. Alekseev; A. B. Smishlyaev; D. A. Tereshko. The solvability of a boundary value problem for time-independent equations of heat and mass transfer under mixed boundary conditions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 66-80. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a5/

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

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

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

[4] Kazhikhov A. V., “Razreshimost nekotorykh odnostoronnikh kraevykh zadach dlya uravnenii Nave–Stoksa”, Dinamika sploshnoi sredy, 16, IG SO AN CCCP, Novosibirsk, 1974, 5–34

[5] Ragulin V. V., “K zadache o protekanii vyazkoi zhidkosti skvoz ogranichennuyu oblast pri zadannom perepade davleniya ili napora”, Dinamika sploshnoi sredy, 27, IG SO AN CSSR, Novosibirsk, 1976, 78–92 | MR

[6] Pironneau O., “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] Bègue C., Conca C., Murat F., Pironneau O., “Les équations de Stokes et de Navier–Stokes avec des conditions aux limites sur la pression”, Nonlinear Partial Different. Equations and their Applic., Lect. Coll. de France Seminar, IX, Paris/Fr., 1985–86; Pitman Res. Notes Math. Ser., 181, 179–264 | MR | Zbl

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

[9] Turek S., Efficient solvers for incompressible flow problems: An algorithmic approach in view of computation problems, LNCSE, 6, Springer, Berlin, 1999 | MR | Zbl

[10] Kobelkov G., Olshanskii M. A., “Effective preconditioning of Uzawa type schemes for a generalized Stokes problem”, Numer. Math., 86:4 (2000), 443–470 | DOI | MR | Zbl

[11] Olshanskii M. A., “Ob odnoi zadache tipa Stoksa s parametrom”, Zh. vychisl. matem. i matem. fiz., 36:2 (1996), 75–86 | MR

[12] Olshanskii M. A., “O zadache Stoksa s modelnymi kraevymi usloviyami”, Matem. sb., 188:4 (1997), 127–144 | MR

[13] Olshanskii M., “An iterative solver for the Oseen problem and the numerical solution of incompressible Navier–Stokes equations”, Numer. Linear Algebra Appl., 6 (1999), 353–378 | 3.0.CO;2-J class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[14] Girault V., “Incompressible finite element methods for Navier–Stokes equations with non-standard boundary conditions in $\mathbb{R}^3$”, Math. Comput., 15 (1988), 55–74 | MR

[15] Bernardi C., Canuto C., Maday Y., “Spectral approximations of the Stokes equations with boundary conditions on the pressure”, SIAM J. Numer. Analys., 28 (1991), 333–362 | DOI | MR | Zbl

[16] Gresho P. M., “Incompressible fluid dynamics: Some fundamental formulations issues”, Ann. Rev. Fluid Mech., 23 (1991), 413–453 | DOI | MR | Zbl

[17] Bramble J. H., Lee P., “On variational formulation for the Stokes equations with nonstandard boundary conditions”, Math. Model. Numer. Analys., 28 (1994), 903–919 | MR | Zbl

[18] Bochev P. B., “Analysis of least-squares finite element methods for the Navier–Stokes equations”, SIAM J. Numer. Analys., 34 (1997), 1817–1844 | DOI | MR | Zbl

[19] Ebmeyer C., Frehse J., Steady Navier–Stokes equations with mixed boundary value conditions in three-dimensional Lipschitzian domains, Preprint, Inst. für angewandte Math. der Univ. Bonn, 1998 | MR

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

[21] Tereshko D. A., “Issledovanie obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii vyazkoi teploprovodnoi zhidkosti”, Dalnevostochnyi matem. sb., 1997, no. 4, 75–85

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

[23] Alekseev G. V., Tereshko D. A., “Statsionarnye zadachi optimalnogo upravleniya dlya uravnenii gidrodinamiki vyazkoi teploprovodnoi zhidkosti”, Sibirskii zh. industr. matem., 1:2 (1998), 24–44 | MR | Zbl

[24] Alekseev G. V., Tereshko D. A., Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teplovoi konvektsii, II, Preprint No 30 IPM DVO RAN, Dalnauka, Vladivostok, 1998

[25] Alekseev G. V., Smishliaev A. B., “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

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

[27] Alekseev G. V., “Razreshimost obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii teplomassoperenosa”, Sibirskii matem. zhurnal, 42:5 (2001), 971–991 | MR | Zbl

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

[29] Hopf E., “Ein all gemeiner Endlichkeitssatz der Hydrodinamik”, Z. Math. Ann., 117 (1940–1941), 764–775 | DOI | MR