Abstract:
We give a description of an abstract scheme of the topological approximation method and mention those fields where its application to concrete models of hydrodynamics yields results. As an illustration, we expose in detail the problem of optimal control of right-hand sides in the initialboundary value problem describing the motion of a viscoelastic incompressible fluid in the Jeffreys model with the Jaumann objective derivative.
Citation:
V. G. Zvyagin, “Topological approximation approach to study of mathematical problems of hydrodynamics”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 2, CMFD, 46, PFUR, M., 2012, 92–119; Journal of Mathematical Sciences, 201:6 (2014), 830–858
\Bibitem{Zvy12}
\by V.~G.~Zvyagin
\paper Topological approximation approach to study of mathematical problems of hydrodynamics
\inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~2
\serial CMFD
\yr 2012
\vol 46
\pages 92--119
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd231}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 201
\issue 6
\pages 830--858
\crossref{https://doi.org/10.1007/s10958-014-2028-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919926064}
Linking options:
https://www.mathnet.ru/eng/cmfd231
https://www.mathnet.ru/eng/cmfd/v46/p92
This publication is cited in the following 33 articles:
A. V. Zvyagin, “On the existence of weak solutions of the Kelvin–Voigt model”, Math. Notes, 116:1 (2024), 130–135
A. S. Ustyuzhaninova, “Ravnomernye attraktory modeli Bingama”, Izv. vuzov. Matem., 2024, no. 8, 65–80
A. S. Ustiuzhaninova, “Uniform Attractors for the Bingham Model”, Russ Math., 68:8 (2024), 56
Victor Zvyagin, Mikhail Turbin, “Weak solvability of the initial-boundary value problem for a finite-order model of the inhomogeneous incompressible Kelvin-Voigt fluid without a positive lower bound on the initial condition of fluid density”, EECT, 2024
V. G. Zvyagin, M. V. Turbin, “Solvability of the initial-boundary value problem for the Kelvin–Voigt fluid motion model with variable density”, Dokl. Math., 107:1 (2023), 9–11
V. G. Zvyagin, M. V. Turbin, “An Existence Theorem for Weak Solutions of the Initial–Boundary Value Problem for the Inhomogeneous Incompressible Kelvin–Voigt Model in Which the Initial Value of Density is Not Bounded from Below”, Math. Notes, 114:4 (2023), 630–634
A. V. Zvyagin, E. I. Kostenko, “Zadacha suschestvovaniya upravleniya s obratnoi svyazyu dlya odnoi drobnoi modeli Foigta”, SMFN, 69, no. 4, Rossiiskii universitet druzhby narodov, M., 2023, 621–642
A. V. Zvyagin, “Uniform Attractors for Non-Autonomous Systems of Nonlinearly Viscous Fluid”, Lobachevskii J Math, 44:3 (2023), 956
Andrey Zvyagin, Ekaterina Kostenko, “Investigation of the Weak Solvability of One Viscoelastic Fractional Voigt Model”, Mathematics, 11:21 (2023), 4472
A. V. Zvyagin, E. I. Kostenko, “On the Existence of Feedback Control for One Fractional Voigt Model”, Diff Equat, 59:12 (2023), 1778
Victor Zvyagin, Mikhail Turbin, “Weak solvability of the initial-boundary value problem for inhomogeneous incompressible Kelvin–Voigt fluid motion model of arbitrary finite order”, J. Fixed Point Theory Appl., 25:3 (2023)
A. V. Zvyagin, “Weak solvability of non-linearly viscous Pavlovsky model”, Russian Math. (Iz. VUZ), 66:6 (2022), 73–78
Andrey Zvyagin, “Solvability of the Non-Linearly Viscous Polymer Solutions Motion Model”, Polymers, 14:6 (2022), 1264
A. V. Zvyagin, “Investigation of the weak solubility of the fractional Voigt alpha-model”, Izv. Math., 85:1 (2021), 61–91
A. V. Zvyagin, “An alpha-model of polymer solutions motion”, Russian Math. (Iz. VUZ), 65:5 (2021), 21–29
Allaberen Ashyralyev, Victor Zvyagin, Andrey Zvyagin, INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2325, INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2021, 020003
Victor Zvyagin, Mikhail Turbin, “Optimal feedback control problem for inhomogeneous Voigt fluid motion model”, J. Fixed Point Theory Appl., 23:1 (2021)
V. G. Zvyagin, A. V. Zvyagin, Nguyen Minh Hong, “Optimal Feedback Control for a Model of Motion
of a Nonlinearly Viscous Fluid”, Diff Equat, 57:1 (2021), 122
V. G. Zvyagin, A. V. Zvyagin, N. M. Khong, “Optimalnoe upravlenie s obratnoi svyazyu dlya odnoi modeli dvizheniya nelineino-vyazkoi zhidkosti”, Chebyshevskii sb., 21:2 (2020), 144–158
Victor Zvyagin, Andrey Zvyagin, Anastasiia Ustiuzhaninova, “Optimal Feedback Control Problem for the Fractional Voigt-α Model”, Mathematics, 8:7 (2020), 1197
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