Inverse Extremal Problems for Stationary Equations of Heat Convection
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 2, pp. 6-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Inverse extremal problems for the stationary heat convection equations are considered. The solvability of these problems is proved, the optimality systems are deduced which describe necessary conditions of the extremum. The sufficient conditions to the data are established which provide the local uniqueness and stability of solutions for specific cost functionals.
@article{VNGU_2006_6_2_a1,
     author = {G. V. Alekseev},
     title = {Inverse {Extremal} {Problems} for {Stationary} {Equations} of {Heat} {Convection}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {6--32},
     year = {2006},
     volume = {6},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a1/}
}
TY  - JOUR
AU  - G. V. Alekseev
TI  - Inverse Extremal Problems for Stationary Equations of Heat Convection
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2006
SP  - 6
EP  - 32
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a1/
LA  - ru
ID  - VNGU_2006_6_2_a1
ER  - 
%0 Journal Article
%A G. V. Alekseev
%T Inverse Extremal Problems for Stationary Equations of Heat Convection
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2006
%P 6-32
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a1/
%G ru
%F VNGU_2006_6_2_a1
G. V. Alekseev. Inverse Extremal Problems for Stationary Equations of Heat Convection. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 2, pp. 6-32. http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a1/

[1] Mohamed Gad-el-Hak, “Flow control”, Appl. Mech. Rev., 42:10 (1989), 261–293 | DOI | MR

[2] M. D. Gunzburger (ed.), Flow control, IMA, 68, Springer, 1995 | MR

[3] M. D. Gunzburger, L. Hou, T. P. Svobodny, “The approximation of boundary control problems for fluid flows with an application to control by heating and cooling”, Comput. Fluids, 22 (1993), 239–251 | DOI | MR | Zbl

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

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

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

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

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

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

[10] Cãpãtin a Anca, Stavre Ruxandra, “A control problem in bioconvective flow”, J. Math. Kyoto Univ. (JMKYAZ), 37:4 (1998), 585–595 | MR

[11] G. V. Alekseev, E. A. Adomavichus, “Theoretical analysis of inverse extremal problems of admixture diffusion in viscous fluids”, J. Inv. Ill-Posed Problems, 9:5 (2001), 435–468 | MR | Zbl

[12] G. V. Alekseev, E. A. Adomavichyus, “O razreshimosti neodnorodnykh kraevykh zadach dlya statsionarnykh uravnenii massoperenosa”, Dalnevost. mat. zhurn., 2:2 (2001), 138–153

[13] G. V. Alekseev, “Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teorii massoperenosa”, Zhurn. vychisl. matem. i matem. fiz., 42:3 (2002), 380–394 | MR | Zbl

[14] G. V. Alekseev, E. A. Adomavichyus, “Issledovanie obratnykh ekstremalnykh zadach dlya nelineinykh statsionarnykh uravnenii perenosa veschestva”, Dalnevost. mat. zhurn., 3:1 (2002), 79–92

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

[16] P. Grisvard, Elliptic problems in nonsmooth domains, Monograph and studies in mathematics, Pitman, London, 1985 | MR | Zbl

[17] A. D. Ioffe, V. M. Tikhomirov, Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR | Zbl

[18] Zh. Sea, Optimizatsiya, teoriya i algoritmy, Mir, M., 1973