An optimal boundary control problem for the motion equations of polymer solutions
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 13-27.

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We study an optimal boundary control problem for stationary equations of a model of the motion of weakly concentrated water solutions of polymers. Sufficient conditions are obtained for the solvability of the problem. Some properties of the set of optimal solutions are established.
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E. S. Baranovskiǐ. An optimal boundary control problem for the motion equations of polymer solutions. Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 13-27. http://geodesic.mathdoc.fr/item/MT_2013_16_2_a1/

[1] Amfilokhiev V. B., Voitkunskii Ya. I., Mazaeva N. P., Khodorkovskii Ya. S., “Techeniya polimernykh rastvorov pri nalichii konvektivnykh uskorenii”, Tr. Leningr. korablestroit. in-ta, 96, 1975, 3–9

[2] Amfilokhiev V. B., Pavlovskii V. A., “Eksperimentalnye dannye o laminarno-turbulentnom perekhode pri techenii polimernykh rastvorov v trubakh”, Tr. Leningr. korablestroit. in-ta, 104, 1976, 3–5

[3] Baranovskii E. S., “Ob optimalnykh zadachakh dlya sistem parabolicheskogo tipa s asferichnymi mnozhestvami dopustimykh upravlenii”, Izv. vuzov. Matem., 2009, no. 12, 74–79 | MR | Zbl

[4] Baranovskii E. S., “Issledovanie matematicheskikh modelei, opisyvayuschikh techeniya zhidkosti Foigta s lineinoi zavisimostyu komponent skorosti ot dvukh prostranstvennykh peremennykh”, Vestnik Voronezhsk. gos. un-ta. Seriya: Fizika. Matematika, 2011, no. 1, 77–93

[5] Goldshtein R. V., Gorodtsov V. A., Mekhanika sploshnykh sred. Ch. I: Osnovy i klassicheskie modeli zhidkostei, Fizmatlit, M., 2000

[6] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, 7-e izd., Fizmatlit, M., 2004 | MR

[7] Ladyzhenskaya O. A., “O globalnoi odnoznachnoi razreshimosti dvumernykh zadach dlya vodnykh rastvorov polimerov”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 28, Zap. nauchn. sem. POMI, 243, 1997, 138–153 | MR | Zbl

[8] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR | Zbl

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

[10] Oskolkov A. P., “O edinstvennosti i razreshimosti v tselom kraevykh zadach dlya uravnenii dvizheniya vodnykh rastvorov polimerov”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 7, Zap. nauchn. sem. LOMI, 38, 1973, 98–136 | MR | Zbl

[11] Oskolkov A. P., “O nestatsionarnykh techeniyakh vyazko-uprugikh zhidkostei”, Kraevye zadachi matematicheskoi fiziki. 12, Tr. MIAN SSSR, 159, 1983, 103–131 | MR | Zbl

[12] Pavlovskii V. A., “K voprosu o teoreticheskom opisanii slabykh vodnykh rastvorov polimerov”, DAN SSSR, 200:4 (1971), 809–813

[13] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | MR | Zbl

[14] Fursikov A. V., Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999 | Zbl

[15] Yushkov E. V., “O razrushenii reshenii zadach gidrodinamicheskogo tipa s singulyarnym istochnikom”, Zh. vychisl. matem. i matem. fiz., 52:8 (2012), 1523–1535 | Zbl

[16] Adams R. A., Fournier John J. F., Sobolev Spaces, 2nd ed., Elsevier/Academic Press, Amsterdam, 2003 | MR