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Sib. Zh. Vychisl. Mat., 2012, Volume 15, Number 4, Pages 409–415 (Mi sjvm490)  

This article is cited in 7 scientific papers (total in 7 papers)

On solutions of the Gol'dshtik problem

D. K. Potapov

St. Petersburg State University, Faculty of Applied Mathematics and Control Processes, St. Petersburg

Abstract: The Gol'dshtik model for separated flows of incompressible fluid is considered. A solution of the given two-dimensional problem in mathematical physics for a finite domain is found with the finite element method. Estimations of the differential operator are obtained. A result on the number of solutions of the Gol'dshtik problem is obtained using the variational method.

Key words: Gol'dshtik problem, nonlinear differential equation, discontinuous nonlinearity, finite element method, variational method, estimations of differential operator, number of solutions.

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English version:
Numerical Analysis and Applications, 2012, 5:4, 342–347

UDC: 517.95
Received: 24.11.2011

Citation: D. K. Potapov, “On solutions of the Gol'dshtik problem”, Sib. Zh. Vychisl. Mat., 15:4 (2012), 409–415; Num. Anal. Appl., 5:4 (2012), 342–347

Citation in format AMSBIB
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\by D.~K.~Potapov
\paper On solutions of the Gol'dshtik problem
\jour Sib. Zh. Vychisl. Mat.
\yr 2012
\vol 15
\issue 4
\pages 409--415
\mathnet{http://mi.mathnet.ru/sjvm490}
\elib{https://elibrary.ru/item.asp?id=20494971}
\transl
\jour Num. Anal. Appl.
\yr 2012
\vol 5
\issue 4
\pages 342--347
\crossref{https://doi.org/10.1134/S1995423912040064}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870416594}


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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. A. V. Vasin, “Opredelenie linii razdela oblastei vikhrevykh techenii”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2013, no. 1, 3–10  mathnet
    2. 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
    3. V. N. Pavlenko, D. K. Potapov, “Existence of solutions to a nonvariational elliptic boundary value problem with parameter and discontinuous nonlinearity”, Siberian Adv. Math., 27:1 (2017), 16–25  mathnet  crossref  crossref  mathscinet  elib
    4. V. N. Pavlenko, D. K. Potapov, “Existence of Three Nontrivial Solutions of an Elliptic Boundary-Value Problem with Discontinuous Nonlinearity in the Case of Strong Resonance”, Math. Notes, 101:2 (2017), 284–296  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. N. Pavlenko, D. K. Potapov, “Elenbaas Problem of Electric Arc Discharge”, Math. Notes, 103:1 (2018), 89–95  mathnet  crossref  crossref  isi  elib
    6. V. N. Pavlenko, D. K. Potapov, “Properties of the spectrum of an elliptic boundary value problem with a parameter and a discontinuous nonlinearity”, Sb. Math., 210:7 (2019), 1043–1066  mathnet  crossref  crossref  adsnasa  isi  elib
    7. V. N. Pavlenko, D. K. Potapov, “On a class of elliptic boundary-value problems with parameter and discontinuous non-linearity”, Izv. Math., 84:3 (2020), 592–607  mathnet  crossref  crossref  isi
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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