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This article is cited in 7 scientific papers (total in 7 papers)
Control problems for equations with a spectral parameter and a discontinuous operator under perturbations
Dmitry K. Potapov St. Petersburg State University, Faculty of Applied Mathematics and Control Processes, St. Petersburg, Russia
Abstract:
In Banach spaces control problems for systems with a spectral parameter, an external perturbation and a discontinuous operator are considered. The theorem on resolvability for investigated problems is proved. General results are applied to control problems for distributed systems of the elliptic type with a spectral parameter and discontinuous nonlinearity under an external perturbation. Propositions on resolvability for such problems are established. Control problem with a perturbation in the Gol'dshtik mathematical model for separated flows of incompressible fluid is considered as an application.
Keywords:
control problems, spectral parameter, discontinuous operator, external perturbation, “perturbation–control–state”, variational method, Gol'dshtik model.
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UDC:
517.98 Received: 17.07.2011 Received in revised form: 01.10.2011 Accepted: 10.01.2012
Citation:
Dmitry K. Potapov, “Control problems for equations with a spectral parameter and a discontinuous operator under perturbations”, J. Sib. Fed. Univ. Math. Phys., 5:2 (2012), 239–245
Citation in format AMSBIB
\Bibitem{Pot12}
\by Dmitry~K.~Potapov
\paper Control problems for equations with a~spectral parameter and a~discontinuous operator under perturbations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2012
\vol 5
\issue 2
\pages 239--245
\mathnet{http://mi.mathnet.ru/jsfu238}
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http://mi.mathnet.ru/eng/jsfu238 http://mi.mathnet.ru/eng/jsfu/v5/i2/p239
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D. K. Potapov, “On solutions of the Gol'dshtik problem”, Num. Anal. Appl., 5:4 (2012), 342–347
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Vistoria V. Yevstafyeva, “Existence of the unique kT-periodic solution for one class of nonlinear systems”, Zhurn. SFU. Ser. Matem. i fiz., 6:1 (2013), 136–142
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Potapov D.K. Yevstafyeva V.V., “Lavrent'Ev Problem for Separated Flows with an External Perturbation”, Electron. J. Differ. Equ., 2013, 255
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Andrei V. Chernov, “O suschestvovanii $\varepsilon$-ravnovesiya v differentsialnykh igrakh, svyazannykh s ellipticheskimi uravneniyami, upravlyaemymi mnogimi igrokami”, MTIP, 6:1 (2014), 91–115
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A. V. Chernov, “O totalnom sokhranenii globalnoi razreshimosti zadachi Gursa dlya upravlyaemogo polulineinogo psevdoparabolicheskogo uravneniya”, Vladikavk. matem. zhurn., 16:3 (2014), 55–63
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A. V. Chernov, “On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation”, Comput. Math. Math. Phys., 55:2 (2015), 212–226
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A. V. Chernov, “On the structure of a solution set of controlled initial-boundary value problems”, Russian Math. (Iz. VUZ), 60:2 (2016), 62–71
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