Abstract:
A modification of a 1D analogue of the Gol'dshtik mathematical model for separated flows of incompressible fluid is considered. The model is a nonlinear differential equation with a boundary condition. Nonlinearity in the equation is continuous and depends on a small parameter. When this parameter tends to zero, we have a discontinuous nonlinearity. The results of the solutions are in accord with the results obtained for the 1D analogue of the Gol'dshtik model for separated flows of incompressible fluid.
Citation:
D. K. Potapov, “A continuous approximation for a 1D analogue of the Gol'dshtik model for separated flows of incompressible fluid”, Sib. Zh. Vychisl. Mat., 14:3 (2011), 291–296; Num. Anal. Appl., 4:3 (2011), 234–238
\Bibitem{Pot11}
\by D.~K.~Potapov
\paper A continuous approximation for a~1D analogue of the Gol'dshtik model for separated flows of incompressible fluid
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 3
\pages 291--296
\mathnet{http://mi.mathnet.ru/sjvm442}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 3
\pages 234--238
\crossref{https://doi.org/10.1134/S1995423911030050}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79960771577}
Linking options:
https://www.mathnet.ru/eng/sjvm442
https://www.mathnet.ru/eng/sjvm/v14/i3/p291
This publication is cited in the following 18 articles:
O. V. Baskov, D. K. Potapov, “On Solutions of the One-Dimensional Goldshtik Problem”, Math. Notes, 115:1 (2024), 12–20
D. K. Potapov, “Variatsionnoe neravenstvo dlya zadachi Shturma–Liuvillya s razryvnoi nelineinostyu”, Sib. elektron. matem. izv., 20:2 (2023), 981–986
O. V. Baskov, D. K. Potapov, “Upravlenie i vozmuschenie v zadache Shturma — Liuvillya s razryvnoi nelineinostyu”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 19:2 (2023), 275–282
D. K. Potapov, “Approximation to the Sturm–Liouville Problem with a Discontinuous Nonlinearity”, Diff Equat, 59:9 (2023), 1185
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
A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “On uniqueness and properties of periodic solution of second-order nonautonomous system with discontinuous nonlinearity”, J. Dyn. Control Syst., 23:4 (2017), 825–837
A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “Existence of subharmonic solutions to a hysteresis system with sinusoidal external influence”, Electron. J. Differ. Equ., 2017, 140
A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “Existence of periodic solutions to automatic control system with relay nonlinearity and sinusoidal external influence”, Int. J. Robust Nonlinear Control, 27:2 (2017), 204–211
A. M. Kamachkin, V. N. Shamberov, G. M. Chitrov, “Special matrix transformations of essential nonlinear control systems”, 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V. F. Demyanov) (CNSA), ed. L. Polyakova, IEEE, 2017, 138–140
A. M. Kamachkin, G. M. Chitrov, V. N. Shamberov, “Normal matrix forms to decomposition and control problems for manydimentional systems”, Vestn. St.-Peterbg. Univ. Ser. 10 Prikl. Mat. Inform. Protsessy, 13:4 (2017), 417–430
Alexander M. Kamachkin, Vladimir N. Shamberov, Gennadiy M. Chitrov, 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017, 1
A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “Non-existence of periodic solutions to non-autonomous second-order differential equation with discontinuous nonlinearity”, Electron. J. Differ. Equ., 2016, 04
Potapov D.K., “Existence of Solutions, Estimates For the Differential Operator, and a “Separating” Set in a Boundary Value Problem For a Second-Order Differential Equation With a Discontinuous Nonlinearity”, Differ. Equ., 51:7 (2015), 967–972
Kamachkin A.M., Chitrov G.M., Shamberov V.N., “Algebraical Aspects of Parametrical Decomposition Method”, 2015 International Conference “Stability and Control Processes” in Memory of V.i. Zubov (Scp), eds. Petrosyan L., Zhabko A., IEEE, 2015, 52–54
Alexander M. Kamachkin, Gennadiy M. Chitrov, Vladimir N. Shamberov, 2015 International Conference “Stability and Control Processes” in Memory of V.I. Zubov (SCP), 2015, 52
Kamachkin A.M., Potapov D.K., Yevstafyeva V.V., “Solution To Second-Order Differential Equations With Discontinuous Right-Hand Side”, Electron. J. Differ. Equ., 2014, 221
Potapov D.K., Yevstafyeva V.V., “Lavrent'Ev Problem for Separated Flows with an External Perturbation”, Electron. J. Differ. Equ., 2013, 255
D. K. Potapov, “On solutions of the Gol'dshtik problem”, Num. Anal. Appl., 5:4 (2012), 342–347
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