Geodesic
Asymptotics of a solution to an optimal boundary control problem in a bounded domain
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 75-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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A problem of optimal boundary control of solutions of an elliptic-type equation with a small coefficient at the Laplace operator and integral constraints on the control in a bounded domain with smooth boundary is considered. A complete asymptotic expansion of the solution of this problem in powers of the small parameter is obtained.
Keywords: singular problems, optimal control, boundary value problems for systems of partial differential equations, asymptotic expansions. 
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A. R. Danilin; A. P. Zorin. Asymptotics of a solution to an optimal boundary control problem in a bounded domain. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 75-82. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a8/

[1] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972, 414 pp. | MR | Zbl

[2] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Izd-vo LGU, L., 1950, 255 pp. | MR

[3] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971, 371 pp. | Zbl

[4] Danilin A. R., Zorin A. P., “Asimptotika resheniya zadachi optimalnogo granichnogo upravleniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 15, no. 4, 2009, 95–107

[5] Danilin A. R., Zorin A. P., “Asimptoticheskoe razlozhenie resheniya zadachi optimalnogo granichnogo upravleniya”, Dokl. AN, 440:4 (2011), 1–4 | MR

[6] Danilin A. R., “Asimptotika ogranichennykh upravlenii dlya singulyarnoi ellipticheskoi zadachi v oblasti s maloi polostyu”, Mat. sb., 189:11 (1998), 27–60 | DOI | MR | Zbl

[7] Danilin A. R., “Approksimatsiya singulyarno vozmuschennoi ellipticheskoi zadachi optimalnogo upravleniya”, Mat. sb., 191:10 (2000), 3–12 | DOI | MR | Zbl

[8] Kapustyan V. E., “Asimptotika ogranichennykh upravlenii v optimalnykh ellipticheskikh zadachakh”, Dokl. AN Ukrainy. Matematika, estestvoznanie, tekhnicheskie nauki, 1992, no. 2, 70–74 | MR

[9] Kapustyan V. E., “Optimalnye bisingulyarnye ellipticheskie zadachi s ogranichennym upravleniem”, Dokl. AN Ukrainy, 1993, no. 6, 81–85 | MR

[10] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964, 540 pp. | MR

[11] Moren K., Metody gilbertova prostranstva, Mir, M., 1965, 570 pp. | MR

[12] Peetre J., “Another approach to elliptic boundary problems”, Comm. Pure. Appl. Math., 14 (1961), 711–731 | DOI | MR | Zbl

[13] Ilin A. M., Soglasovanie asimptotichesk ikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989, 336 pp. | MR

[14] Vishik M. I., Lyusternik L. A., “Regulyaronoe vyrozhdenie i pogranichnyi sloi dlya lineinykh differentsialnykh uravnenii s malym parametrom”, Uspekhi mat. nauk, 12:5 (1957), 3–122 | MR | Zbl

[15] Ilin A. M., “Pogranichnyi sloi”, Itogi nauki i tekhniki. Sovremen. poblemy matematiki. Fundamentalnye napravleniya, 34, VINITI AN SSSR, M., 1988, 175–213 | MR | Zbl