Geodesic
Approximation of optimal control problems for semi-linear elliptic convection-diffusion equations with discontinuous coefficients and states, with controls involved in the coefficients of diffusion and convective transfer
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 54-69.

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

In this paper we study main problems of approximation of nonlinear optimal control problems described by elliptic convection-diffusion equations with discontinuous coefficients and solutions, with controls involved in the coefficients of diffusion and convective transfer. Issues of discrete optimization problems construction, convergence of the approximations with respect to state, functional and control, and regularization of approximations are considered.
Keywords: the problem of optimal control, semi-linear elliptic equations, difference method.
Mots-clés : convective and diffusion transfer 
@article{SVMO_2016_18_1_a6,
     author = {F. V. Lubyshev and A. R. Manapova and M. \`E. Fairuzov},
     title = {Approximation of optimal control problems for semi-linear elliptic convection-diffusion equations with discontinuous coefficients and states, with controls involved in the coefficients of diffusion and convective transfer},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {54--69},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a6/}
}
TY  - JOUR
AU  - F. V. Lubyshev
AU  - A. R. Manapova
AU  - M. È. Fairuzov
TI  - Approximation of optimal control problems for semi-linear elliptic convection-diffusion equations with discontinuous coefficients and states, with controls involved in the coefficients of diffusion and convective transfer
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2016
SP  - 54
EP  - 69
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a6/
LA  - ru
ID  - SVMO_2016_18_1_a6
ER  - 
%0 Journal Article
%A F. V. Lubyshev
%A A. R. Manapova
%A M. È. Fairuzov
%T Approximation of optimal control problems for semi-linear elliptic convection-diffusion equations with discontinuous coefficients and states, with controls involved in the coefficients of diffusion and convective transfer
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2016
%P 54-69
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a6/
%G ru
%F SVMO_2016_18_1_a6
F. V. Lubyshev; A. R. Manapova; M. È. Fairuzov. Approximation of optimal control problems for semi-linear elliptic convection-diffusion equations with discontinuous coefficients and states, with controls involved in the coefficients of diffusion and convective transfer. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 54-69. http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a6/

[1] Samarskii A. A., Vabischevich P. N., Vychislitelnaya teploperedacha, Knizhnyi dom «LIBROKOM», M., 2009

[2] 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”, Zhurnal vychisl. matem. i matem. fiziki, 47:3 (2007), 376–396 | MR | Zbl

[3] Lubyshev F. V., “O raznostnykh approksimatsiyakh zadach optimalnogo upravleniya dlya polulineinykh ellipticheskikh uravnenii s razryvnymi koeffitsientami i resheniyami”, Zhurnal vychisl. matem. i matem. fiziki, 52:8 (2012), 1378–1399 | MR | Zbl

[4] Lubyshev F. V., Manapova A. R., Fairuzov M. E., “Approksimatsii zadach optimalnogo upravleniya dlya polulineinykh ellipticheskikh uravnenii s razryvnymi koeffitsientami i resheniyami, s upravleniem v granichnykh usloviyakh sopryazheniya”, Zhurnal vychisl. matem. i matem. fiziki, 54:11 (2014), 1767–1792 | DOI | MR | Zbl

[5] Lubyshev F. V., Fairuzov M. E., “Approksimatsii zadach optimalnogo upravleniya dlya polulineinykh ellipticheskikh uravnenii s razryvnymi koeffitsientami i sostoyaniyami, s upravleniyami v koeffitsientakh pri starshikh proizvodnykh”, Zhurnal vychisl. matem. i matem. fiziki, 56:7 (2016), 70–96 | MR

[6] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, SO AN SSSR, Novosibirsk, 1962 | MR

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

[8] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[9] Kufner A., Fuchik F., Nelineinye differentsialnye uravneniya, Nauka, M., 1988 | MR

[10] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR

[11] Kinderleler D., Stampakkya G., Vvedenie v variatsionnye neravenstva i ikh prilozheniya, Mir, M., 1983 | MR

[12] Rektoris K., Variatsionnye metody v matematicheskoi fizike i tekhnike, Mir, M., 1985 | MR

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

[14] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[15] Brauder F.E., Materialy k sovmestnomu sovetsko-amerikanskomu simpoziumu po uravneniyam s chastnymi proizvodnymi, Novosibirsk, 1963

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

[17] Samarskii A. A., Andreev V. B., Raznostnye metody dlya ellipticheskikh uravnenii, Nauka, M., 1976 | MR

[18] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989 | MR

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

[20] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002 | MR

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