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J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 2, Pages 239–245 (Mi jsfu238)  

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.

Full text: PDF file (163 kB)
References: PDF file   HTML file
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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. K. Potapov, “On solutions of the Gol'dshtik problem”, Num. Anal. Appl., 5:4 (2012), 342–347  mathnet  crossref  elib
    2. 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  mathnet
    3. Potapov D.K. Yevstafyeva V.V., “Lavrent'Ev Problem for Separated Flows with an External Perturbation”, Electron. J. Differ. Equ., 2013, 255  mathscinet  zmath  isi  elib
    4. Andrei V. Chernov, “O suschestvovanii $\varepsilon$-ravnovesiya v differentsialnykh igrakh, svyazannykh s ellipticheskimi uravneniyami, upravlyaemymi mnogimi igrokami”, MTIP, 6:1 (2014), 91–115  mathnet
    5. A. V. Chernov, “O totalnom sokhranenii globalnoi razreshimosti zadachi Gursa dlya upravlyaemogo polulineinogo psevdoparabolicheskogo uravneniya”, Vladikavk. matem. zhurn., 16:3 (2014), 55–63  mathnet
    6. 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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. 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  mathnet  crossref  isi
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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