Geodesic
Optimal feedback control for a thermoviscoelastic model of the motion of water polymer solutions
Matematičeskie trudy, Tome 21 (2018) no. 2, pp. 181-203.

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We study an optimal feedback control problem for an initial boundary value problem of a thermoviscoelastic model describing the motion of weakly concentrated water polymer solutions in the presence of dependence of the viscosity on the temprature. We prove the existence of an optimal solution minimizing to a given bounded lower semicontinuous quality functional. For proving the existence of an optimal solution, we use the topological approximation method for studying problems in hydrodynamics. 
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V. G. Zvyagin; A. V. Zvyagin. Optimal feedback control for a thermoviscoelastic model of the motion of water polymer solutions. Matematičeskie trudy, Tome 21 (2018) no. 2, pp. 181-203. http://geodesic.mathdoc.fr/item/MT_2018_21_2_a8/

[1] Antontsev S. N., Kazhikhov A. V., Monakhov V. N., Kraevye zadachi mekhaniki neodnorodnykh zhidkostei, Nauka, Novosibirsk, 1983 | MR

[2] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., Vvedenie v teoriyu mnogoznachnykh otobrazhenii i differentsialnykh vklyuchenii, Knizhnyi dom «Librokom», M., 2011 | MR

[3] Vorovich I. I., Yudovich V. I., “Statsionarnye techeniya vyazkoi neszhimaemoi zhidkosti”, Matem. sb., 53(95):4 (1961), 393–428

[4] Zvyagin V. G., “Approksimatsionno-topologicheskii podkhod k issledovaniyu matematicheskikh zadach gidrodinamiki”, Sovremennaya matematika. Fundamentalnye napravleniya (SMFN), 46, 2012, 92–119

[5] Zvyagin A. V., “Zadacha optimalnogo upravleniya s obratnoi svyazyu dlya matematicheskoi modeli dvizheniya slabo kontsentrirovannykh vodnykh polimernykh rastvorov s ob'ektivnoi proizvodnoi”, Sib. matem. zhurn., 54:4 (2013), 807–825 | MR | Zbl

[6] Zvyagin A. V., “Issledovanie razreshimosti termovyazkouprugoi modeli, opisyvayuschei dvizhenie slabo kontsentrirovannykh vodnykh rastvorov polimerov”, Sib. matem. zhurn., 59:5 (2018), 1066–1085

[7] Zvyagin V. G., Turbin M. V., Matematicheskie voprosy gidrodinamiki vyazkouprugikh sred, «KRASAND» (URSS), M., 2012

[8] Zvyagin A. V., Orlov V. P., “Issledovanie razreshimosti zadachi termovyazkouprugosti dlya lineino uprugo-zapazdyvayuschei zhidkosti Foigta”, Matem. zametki, 97:5 (2015), 681–698 | DOI | MR | Zbl

[9] Ladyzhenskaya O. A., Matematicheskaya teoriya vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970

[10] Oskolkov A. P., “O nekotorykh kvazilineinykh sistemakh, vstrechayuschikhsya pri izuchenii dvizheniya vyazkikh zhidkostei”, Zap. nauchn. sem. LOMI, 52, 1975, 128–157 | Zbl

[11] Temam R., Uravneniya Nave — Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981

[12] Filippov A. F., “O nekotorykh voprosakh teorii optimalnogo regulirovaniya”, Vestn. MGU. Ser. 14, 1959, no. 2, 25–32 | Zbl

[13] Fursikov A. V., Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Universitetskaya ser., 5, Nauchnaya kniga, Novosibirsk, 1999

[14] Aubin J.-P., Cellina A., Differential Inclusions. Set-Valued Maps and Viability Theory, Springer-Verlag, Berlin etc., 1984 | MR | Zbl

[15] Choi H., Temam R., Moin P., Kim J., “Feedback control for unsteady flow and its application to the stochastic Burgers equation”, J. Fluid Mech., 253 (1993), 509–543 | DOI | MR | Zbl

[16] Simon J., “Compact sets in the space $L^p(0,T; B)$”, Ann. Mat. Pura Appl., 146 (1987), 65–96 | DOI | MR | Zbl

[17] Zvyagin A. V., “Solvability for equations of motion of weak aqueous polymer solutions with objective derivative”, Nonlinear Anal., Theory Methods Appl. Ser. A, 90 (2013), 70–85 | DOI | MR | Zbl

[18] Zvyagin A. V., “Solvability of the stationary mathematical model of a non-Newtonian fluid motion with the objective derivative”, Fixed Point Theory, 15:2 (2014), 623–634 | MR | Zbl

[19] Zvyagin V., Obukhovskii V., Zvyagin A., “On inclusions with multivalued operators and their applications to some optimization problems”, J. Fixed Point Theory Appl., 16:1–2 (2014), 27–82 | DOI | MR | Zbl

[20] Zvyagin V. G., Orlov V. P., “On certain mathematical models in continuum thermomechanics”, J. Fixed Point Theory Appl., 15:1 (2014), 3–47 | DOI | MR | Zbl

[21] Zvyagin V. G., Orlov V. P., “Solvability of a parabolic problem with non-smooth data”, J. Math. Anal. Appl., 453:1 (2017), 589–606 | DOI | MR | Zbl

[22] Zvyagin V. G., Turbin M. V., “Optimal feedback control in the mathematical model of low concentrated aqueous polymer solutions”, J. Optim. Theory Appl., 148:1 (2011), 146–163 | DOI | MR | Zbl