Optimal feedback control for one motion model of a nonlinearly viscous fluid
Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 144-158.

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

An optimal control problem with a feedback is considered for an initial boundary problem describing a motion of non-linearly viscous liquid. An existence of an optimal solution minimising a given quality functional is proved. A topological approximation approach to study of mathematical problems of hydrodynamics is used in the proof of existence of an optimal solution.
Keywords: optimal control with feedback, existence theorem, nonlinearly viscous fluid.
@article{CHEB_2020_21_2_a11,
     author = {V. G. Zvyagin and A. V. Zvyagin and N. M. Hong},
     title = {Optimal feedback control for one motion model of a nonlinearly viscous fluid},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {144--158},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a11/}
}
TY  - JOUR
AU  - V. G. Zvyagin
AU  - A. V. Zvyagin
AU  - N. M. Hong
TI  - Optimal feedback control for one motion model of a nonlinearly viscous fluid
JO  - Čebyševskij sbornik
PY  - 2020
SP  - 144
EP  - 158
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a11/
LA  - ru
ID  - CHEB_2020_21_2_a11
ER  - 
%0 Journal Article
%A V. G. Zvyagin
%A A. V. Zvyagin
%A N. M. Hong
%T Optimal feedback control for one motion model of a nonlinearly viscous fluid
%J Čebyševskij sbornik
%D 2020
%P 144-158
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a11/
%G ru
%F CHEB_2020_21_2_a11
V. G. Zvyagin; A. V. Zvyagin; N. M. Hong. Optimal feedback control for one motion model of a nonlinearly viscous fluid. Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 144-158. http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a11/

[1] Litvinov V. G., Motion of nonlinear viscous fluid, Nauka, M., 1982 | MR

[2] Sobolevskii P. E., “The Existence of Solutions of a Mathematical Model of a Nonlinear Viscous Fluid”, Doklady Akademii Nauk SSSR, 285 (1985), 44–48 | MR

[3] Dmitrienko V. T., Zvyagin V. G., “The topological degree method for equations of the Navier–Stokes type”, Abstract and Applied Analysis, 2:1 (1997), 1–45 | DOI | MR | Zbl

[4] Zvyagin V. G., Treasurer M. V., “Attractors of an autonomous model of a nonlinearly viscous fluid”, Doklady RAS, 2020

[5] Lions J. L., Optimal control of systems governed by partial differential equations, Springer, Berlin, 1971 | MR | Zbl

[6] Abergel F., Temam R., “On some control problems in fluid mechanics”, Theor. Comput. Fluid Dyn., 1:6 (1990), 303–325 | DOI | Zbl

[7] Fursikov A. V., Optimal Control of Distributed Systems. Theory and Applications, Transl. Math. Monogr., 187, Amer. Math. Soc., Providence, RI, 2000 | MR | Zbl

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

[9] Zvyagin A. V., “Optimal feedback control for a thermoviscoelastic model of Voigt fluid motion”, Dokl. Math., 93:3 (2016), 270–272 | DOI | MR | Zbl

[10] Zvyagin A. V., “Optimal feedback control for Leray and Navier-Stokes alpha models”, Dokl. Math., 99:3 (2019), 299–302 | DOI | MR | Zbl

[11] Zvyagin V. G., “Topological approximation approach to study of mathematical problems of hydrodynamics”, J. Math. Sci., 201:6 (2014), 830–858 | DOI | MR | Zbl

[12] Zvyagin V. G., Turbin M. V., Mathematical problems in the hydrodynamics of viscoelastic media, KRASAND, M., 2012

[13] Temam R., Navier-Stokes Equation: Theory and Numerical Analysis, North-Holland, 1977 | MR

[14] Zvyagin V. G., Dmitrienko V. T., Topological Approximation Approach to the Study of Hydrodynamical Problems. The Navier-Stokes System, URSS Editorial, M., 2004 (in Russian)

[15] Ficker G., Existence Theorems in the Theory of Elasticity, Russian translation, Mir, M., 1974

[16] Gajewski H., Gröger K., Zacharias K., Nichtlineare operatorgleichungen und operator differentialgleichungen, Akad Verlag, Berlin, 1974 | MR

[17] Kamenskii M., Obukhovskii V., Zecca P., Condensing multivalued maps and semilinear differential inclusions in Banach spaces, Walter de Gruyter, Berlin, 2001 | MR