Geodesic
Accuracy estimate with respect to state of finite-dimensional approximations for optimization problems for semi-linear elliptic equations with discontinuous coefficients and solutions
Ufa mathematical journal, Tome 6 (2014) no. 3, pp. 69-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the work we consider nonlinear optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions with control in the conjugation boundary conditions. We construct difference approximations for extremum problems and obtain the estimates for approximation accuracy with respect to the state.
Keywords: optimal control problem, semi-linear elliptic equations, difference method of solving. 
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A. R. Manapova; F. V. Lubyshev. Accuracy estimate with respect to state of finite-dimensional approximations for optimization problems for semi-linear elliptic equations with discontinuous coefficients and solutions. Ufa mathematical journal, Tome 6 (2014) no. 3, pp. 69-84. http://geodesic.mathdoc.fr/item/UFA_2014_6_3_a4/

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

[2] Ishmukhametov A. Z., Voprosy ustoichivosti i approksimatsii zadach optimalnogo upravleniya, VTs RAN, M., 1999

[3] Ishmukhametov A. Z., Voprosy ustoichivosti i approksimatsii zadach optimalnogo upravleniya sistemami s raspredelennymi parametrami, VTs RAN, M., 2001 | MR

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

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

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

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

[8] Tsurko V. A., “O tochnosti raznostnykh skhem dlya parabolicheskikh uravnenii s razryvnym resheniem”, Differents. ur-niya, 36:7 (2000), 986–992 | MR | Zbl

[9] Tsurko V. A., “Raznostnye metody dlya zadach konvektsii-diffuzii s razryvnymi koeffitsientami i resheniyami”, Differents. ur-niya, 41:2 (2005), 274–280 | 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., Fairuzov M. E., “Approksimatsiya i regulyarizatsiya zadach optimalnogo upravleniya dlya kvazilineinykh ellipticheskikh uravnenii”, Zhurnal vychisl. matem. i matem. fiziki, 41:8 (2001), 1148–1164 | MR | Zbl

[12] 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

[13] Lubyshev F. V., Manapova A. R., “Raznostnye approksimatsii zadach optimizatsii dlya polulineinykh ellipticheskikh uravnenii v vypukloi oblasti s upravleniyami v koeffitsientakh pri starshikh proizvodnykh”, Zhurnal vychisl. matem. i matem. fiziki, 53:1 (2013), 20–46 | DOI | MR | Zbl

[14] Kartashov E. M., Analiticheskie metody v teorii teploprovodnosti tverdykh tel, Vysshaya shkola, M., 1985

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

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

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

[18] Kufner A., Fuchik S., Nelineinye differentsialnye uravneniya, Nauka, M., 1988 | MR | Zbl

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

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

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

[22] Drenska N. T., “Tochnost chislennykh algoritmov dlya odnomernoi zadachi ob ostyvanii metalla v formakh”, Vestnik Moskovsk. universiteta. Ser. 15. Vychislit. matem. i kibernetika, 1981, no. 4, 15–21 | MR | Zbl