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JOURNALS // Zapiski Nauchnykh Seminarov POMI

Zap. Nauchn. Sem. POMI, 2018, Volume 477, Pages 54–86 (Mi znsl6737)

Optimal feedback control problem for the Bingam model with periodical boundary conditions on spatial variables
V. G. Zvyagin, A. V. Zvyagin, M. V. Turbin

References

1. V. V. Shelukhin, “Bingham Viscoplastic as a Limit of Non-Newtonian Fluids”, J. Math. Fluid Mechanic, 4:2 (2002), 109–127  crossref  mathscinet  zmath  adsnasa
2. G. Dyuvo, Zh.-L. Lions, Neravenstva v mekhanike i fizike, Nauka, M., 1980
3. J. U. Kim, “On the Initial-Boundary Value Problem for a Bingham Fluid in a Three Dimensional Domain”, Trans. Amer. Math. Soc., 304:2 (1987), 751–770  mathscinet  zmath
4. G. A. Seregin, “O dinamicheskoi sisteme, porozhdennoi dvumernymi uravneniyami dvizheniya sredy Bingama”, Zap. nauchn. sem. LOMI, 188, 1991, 128–142  mathnet
5. J. L. Lions, Optimal control of systems governed by partial differential equations, Springer, Berlin, 1971  mathscinet  zmath
6. F. Abergel, R. Temam, “On Some Control Problems in Fluid Mechanics”, Theor. Comput. Fluid Dyn., 1:6 (1990), 303–325  crossref  zmath
7. M. D. Gunzburger, L. Hou, T. P. Svobodny, “Boundary velocity control of incompressible flow with an application to viscous drag reduction”, SIAM J. Control Optim., 30:1 (1992), 167–181  crossref  mathscinet  zmath  adsnasa
8. A. V. Fursikov, Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Universitetskaya seriya, 5, Nauchnaya kniga, Novosibirsk, 1999
9. H. Choi, R. Temam, P. Moin, J. Kim, “Feedback control for unsteady flow and its application to Burgers equation”, J. Fluid Mech., 253 (1993), 509–543  crossref  mathscinet  zmath  adsnasa
10. V. V. Obukhovskii, P. Zecca, V. G. Zvyagin, “Optimal feedback control in the problem of the motion of a viscoelastic fluid”, Topological Methods in Nonlinear Analysis, 23:2 (2004), 323–337  crossref  mathscinet  zmath
11. V. G. Zvyagin, M. V. Turbin, “Optimal Feedback Control in the Mathematical Model of Low Concentrated Agueous Polymer Solutions”, J. Optimization Theory and Applications, 148:1 (2011), 146–163  crossref  mathscinet  zmath
12. V. G. Zvyagin, M. Yu. Kuz'min, “On an optimal control problem in the Voight model of the motion of a viscoelastic fluid”, J. Math. Sci., 149:5 (2008), 1618–1627  mathnet  crossref  mathscinet
13. V. Zvyagin, V. Obukhovskii, A. Zvyagin, “On inclusions with multivalued operators and their applications to some optimization problems”, J. Fixed Point Theory and Applications, 16 (2014), 27–82  crossref  mathscinet  zmath
14. A. V. Zvyagin, “Zadacha optimalnogo upravleniya s obratnoi svyazyu dlya matematicheskoi modeli dvizheniya slabo kontsentrirovannykh vodnykh polimernykh rastvorov s ob'ektivnoi proizvodnoi”, Sib. matem. zhurnal, 54:4 (2013), 807—825  mathnet  mathscinet  zmath
15. A. V. Zvyagin, “Optimalnoe upravlenie s obratnoi svyazyu dlya termovyazkouprugoi modeli dvizheniya zhidkosti Foigta”, Dokl. Akademii Nauk, 468:3 (2016), 251–253  crossref  zmath
16. M. A. Krasnoselskii, P. P. Zabreiko, P. E. Sobolevskii, E. I. Pustylnik, Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1970  mathscinet
17. R. Temam, “Navier-Stokes equations and nonlinear functional analysis”, CBM-NSF Regional Conference Series in Applied Mathematics, Philadelphia, Pennsylvania, 1983  mathscinet
18. V. G. Zvyagin, “Topological Approximation Approach to Study of Mathematical Problems of Hydrodynamics”, J. Math. Sci., 201:6 (2014), 830–858  mathnet  crossref  mathscinet  zmath
19. V. G. Zvyagin, M. V. Turbin, Matematicheskie voprosy gidrodinamiki vyazkouprugikh sred, KRASAND, M., 2012
20. J. L. Lions, E. Magenes, Problemès aux limites non homogènes et applications, v. 1, Dunod, Paris, 1968  mathscinet  zmath
21. R. Temam, Uravneniya Nave-Stoksa. Teoriya i chislennyi analiz, Mir, M., 1987


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