Geodesic
Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1, pp. 20-46 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Finite difference approximations are proposed for nonlinear optimal control problems for a non-self-adjoint elliptic equation with Dirichlet boundary conditions in a convex domain $\Omega\subset\mathbb{R}^2$ with controls involved in the leading coefficients. The convergence of the approximations with respect to the state, functional, and control is analyzed, and a regularization of the approximations is proposed. 
@article{ZVMMF_2013_53_1_a2,
     author = {F. V. Lubyshev and A. R. Manapova},
     title = {Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {20--46},
     year = {2013},
     volume = {53},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a2/}
}
TY  - JOUR
AU  - F. V. Lubyshev
AU  - A. R. Manapova
TI  - Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 20
EP  - 46
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a2/
LA  - ru
ID  - ZVMMF_2013_53_1_a2
ER  - 
%0 Journal Article
%A F. V. Lubyshev
%A A. R. Manapova
%T Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 20-46
%V 53
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a2/
%G ru
%F ZVMMF_2013_53_1_a2
F. V. Lubyshev; A. R. Manapova. Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1, pp. 20-46. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a2/

[1] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972 | MR

[2] Alifanov O. M., Artyukhin E. A., Rumyantsev S. V., Ekstremalnye metody resheniya nekorrektnykh zadach, Nauka, M., 1988 | MR | Zbl

[3] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[4] Potapov M. M., Approksimatsiya ekstremalnykh zadach v matematicheskoi fizike (giperbolicheskie uravneniya), Izd-vo MGU, M., 1985

[5] Ishmukhametov A. Z., Voprosy ustoichivosti i approksimatsii zadach optimalnogo upravleniya, Izd-vo VTs RAN, M., 1999

[6] Ishmukhametov A. Z., Voprosy ustoichivosti i approksimatsii zadach optimalnogo upravleniya sistemami s raspredelennymi parametrami, Izd-vo VTs RAN, M., 2001

[7] Lubyshev F. V., Raznostnye approksimatsii zadach optimalnogo upravleniya sistemami, opisyvaemymi uravneniyami v chastnykh proizvodnykh, BGU, Ufa, 1999

[8] Lubyshev F. V., “Approksimatsiya i regulyarizatsiya zadach optimalnogo upravleniya dlya nesamosopryazhennogo ellipticheskogo uravneniya s peremennymi koeffitsientami”, Zh. vychisl. matem. i matem. fiz., 31:1 (1991), 17–30 | MR | Zbl

[9] Lubyshev F. V., “Approksimatsiya i regulyarizatsiya zadach optimalnogo upravleniya koeffitsientami parabolicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 33:8 (1993), 1166–1183 | MR | Zbl

[10] Lubyshev F. V., “Approksimatsiya i regulyarizatsiya zadach optimalnogo upravleniya dlya parabolicheskikh uravnenii s upravleniyami v koeffitsientakh”, Dokl. RAN, 349:5 (1996), 598–602 | MR | Zbl

[11] Lubyshev F. V., Manapova A. R., “O nekotorykh zadachakh optimalnogo upravleniya i ikh raznostnykh approksimatsiyakh i regulyarizatsii dlya kvazilineinykh ellipticheskikh uravnenii s upravleniyami v koeffitsientakh”, Zh. vychisl. matem. i matem. fiz., 47:3 (2007), 376–394 | MR

[12] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[13] Oganesyan L. A., Rukhovets L. A., Variatsionno-raznostnye metody resheniya ellipticheskikh uravnenii, Izd-vo ArmSSR, Erevan, 1979

[14] Samarskii A. A., Lazarov R. D., Makarov V. L., Raznostnye skhemy dlya differentsialnykh uravnenii s obobschennymi resheniyami, Vyssh. shkola, M., 1987

[15] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1986 | MR | Zbl