Geodesic
Solvability of inhomogeneous boundary problems for the stationary mass-transfer equations
Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 138-153.

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

Boundary value problems for stationary mass-transfer for viscous equations are considered under nhomogeneous boundary conditions for the velocity and the concentration of the substance. The existence and uniqueness of a weak solution of the initial boundary value problem in a domain with a Lipshitz boundary is proved, exact apriori estimates of the solution are deduced and the regularity of the solution in the case of two dimensions is studied. 
@article{DVMG_2001_2_2_a12,
     author = {G. V. Alekseev and E. A. Adomavichus},
     title = {Solvability of inhomogeneous boundary problems for the stationary mass-transfer equations},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {138--153},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a12/}
}
TY  - JOUR
AU  - G. V. Alekseev
AU  - E. A. Adomavichus
TI  - Solvability of inhomogeneous boundary problems for the stationary mass-transfer equations
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2001
SP  - 138
EP  - 153
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a12/
LA  - ru
ID  - DVMG_2001_2_2_a12
ER  - 
%0 Journal Article
%A G. V. Alekseev
%A E. A. Adomavichus
%T Solvability of inhomogeneous boundary problems for the stationary mass-transfer equations
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2001
%P 138-153
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a12/
%G ru
%F DVMG_2001_2_2_a12
G. V. Alekseev; E. A. Adomavichus. Solvability of inhomogeneous boundary problems for the stationary mass-transfer equations. Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 138-153. http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a12/

[1] D. Dzhozef, Ustoichivost dvizhenii zhidkosti, Mir, M., 1981, 640 pp.

[2] G. I. Marchuk, Matematicheskoe modelirovanie v probleme okruzhayuschei sredy, Nauka, M., 1982, 319 pp. | MR

[3] E. A. Adomavichyus, G. V. Alekseev, Teoreticheskii analiz obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii massoperenosa, Preprint No 7 IPM DVO RAN, Dalnauka, Vladivostok, 1999, 44 pp.

[4] M. Gaultier and M. Lezaun, “Equation de Navier-Stokes couplees a des equation de la chaleur: resolution par une methode de point fixe en dimension”, Ann. Sc. Math., 13 (1989), 1–17, Quebec | MR | Zbl

[5] F. Abergel and E. Casas, “Some optimal control problems of multistate equation appearing in fluid mechanics”, Math. Modeling Numer. Anal., 27 (1993), 223–247 | MR | Zbl

[6] E. Casas, “Optimality conditions for some control problems of turbulent flows”, Flow control. IMA 68, ed. M. D. Gunzburger, Springer, 1995, 127–147 (to appear) | MR | Zbl

[7] G. V. Alekseev, Teoreticheskii analiz statsionarnykh zadach granichnogo upravleniya dlya uravnenii teplovoi konvektsii, Preprint No 16 IPM DVO RAN, Dalnauka, Vladivostok, 1996, 64 pp.

[8] G. V. Alekseev, “Statsionarnye zadachi granichnogo upravleniya dlya uravnenii teplovoi konvektsii”, Dokl. RAN, 362:2 (1998), 174–177 | MR | Zbl

[9] G. V. Alekseev, “Razreshimost statsionarnykh zadach granichnogo upravleniya dlya uravnenii teplovoi konvektsii”, Sib. mat. zhurn., 39:5 (1998), 982–998 | MR | Zbl

[10] K. Ito, S. S. Ravindran, “Optimal control of thermally convected fluid flows”, SIAM J. Sci. Comput., 19:6 (1998), 1847–1869 | DOI | MR | Zbl

[11] H. C. Lee and O. Yu. Imanuilov, “Analysis of optimal control problems for the 2-D stationary Boussinesq equations”, J. Math. Anal. Appl., 242:2 (2000), 191–211 | DOI | MR | Zbl

[12] Kan-On Yukio, Narukawa Kimiaki and Teramoto Yoshiaki, “On the equations of biconvective flow”, J. Math. Kyoto Univ. (JMKYAZ), 32:1 (1992), 135–153 | MR | Zbl

[13] A. Cãpãtinã, R. Stavre, “A control problem in bioconvective flow”, J. Math. Kyoto Univ. (JMKYAZ), 37:4 (1998), 585–595

[14] Zh.-P. Oben, Priblizhennoe reshenie ellipticheskikh kraevykh zadach, Mir, M., 1977 | MR

[15] U. Rudin, Funktsionalnyi analiz, Mir, M., 1975 | MR

[16] V. Girault, P.-A. Raviart, Finite element methods for Navier-Stokes equations, Theory and algorithms, Springer-Verlag, Berlin, 1986, 376 pp. | MR | Zbl

[17] J. Necǎs, Les Méthodes Directes en Theorie des Equations Elliptiques, Masson, 1967 | MR

[18] E. Casas, L. Fernández, “A Green's formula for quasilinear elliptic operators”, J. Math. Anal. Appl., 142 (1989), 62–72 | DOI | MR

[19] G. V. Alekseev, Obratnye zadachi obnaruzheniya istochnikov primesi v vyazkikh zhidkostyakh, Preprint No 8 IPM DVO RAN, Dalnauka, Vladivostok, 1999, 57 pp.

[20] G. V. Alekseev, D. A. Tereshko, Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teplovoi konvektsii, Preprint No 9 IPM DVO RAN, Dalnauka, Vladivostok, 1997, 56 pp.

[21] G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations, v. II, Nonlinear Steady Problems, Springer-Verlag, New York, 1994 | MR

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

[23] D. S. Jerison, C. E. Kenig, “The inhomogeneous Dirichlet problem in Liptschitz domains”, J. Funct. Anal., 130 (1995), 169–219 | DOI | MR

[24] D. S. Jerison, C. E. Kenig, “The Neumann problem on Lipschitz domains”, Bull. Amer. Math. Soc., 4 (1981), 203–207 | DOI | MR | Zbl

[25] G. Savare, “Regularity results for elliptic equations in Lipschitz domains”, J. Funct. Anal., 152 (1998), 176–201 | DOI | MR | Zbl

[26] G. Savare, “Regularity and perturbation results for mixed second order elliptic problems”, Comm. Partial Diff. Eq., 22 (1997), 869–899 | DOI | MR | Zbl