01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
17.11.1979
E-mail:
Keywords:
Fluid dynamics, weak solution, existence theorem, attractor
UDC:
571.988, 532, 515.126.4
Subject:
Study of the solvability and qualitative behavior of solutions to initial-boundary value problems of non-Newtonian fluid dynamics
Main publications:
V. G. Zvyagin, M. V. Turbin, Matematicheskie voprosy gidrodinamiki vyazkouprugikh sred, KRASAND, M., 2012
V. G. Zvyagin, M. V. Turbin, “Issledovanie nachalno-kraevykh zadach dlya matematicheskikh modelei dvizheniya zhidkostei Kelvina-Foigta”, Sovremennaya matematika. Fundamentalnye napravleniya, 31 (2009), 3-144
V. Zvyagin, M. Turbin, “Weak solvability of the initial-boundary value problem for inhomogeneous incompressible Kelvin-Voigt fluid motion model of arbitrary finite order”, Journal of Fixed Point Theory and Applications, 25:3 (2023), Article number 63
M. Turbin, A. Ustiuzhaninova, “Existence of weak solution to initial-boundary value problem for finite order Kelvin-Voigt fluid motion model”, Boletín de la Sociedad Matemática Mexicana, 29:2 (2023), Article number 54
M. Turbin, A. Ustiuzhaninova, “Trajectory and Global Attractors for the Kelvin-Voigt Model Taking into Account Memory along Fluid Trajectories”, Mathematics, 12:2 (2024), Article number 266
M. Turbin, A. Ustiuzhaninova, “Trajectory and Global Attractors for the Kelvin-Voigt Model Taking into Account Memory along Fluid Trajectories”, Mathematics, 12:2 (2024), 266 , 26 pp.
2.
M. V. Turbin, A. S. Ustiuzhaninova, “Solvability of an Initial-Boundary Value Problem for the Modified Kelvin-Voigt Model with Memory along Fluid Motion Trajectories”, Differential Equations, 60 (2024), 180-203
3.
V. G. Zvyagin, A. V. Zvyagin, V. P. Orlov, M. V. Turbin, “On the Weak Solvability of High-order Viscoelastic Fluid Dynamics Model”, Lobachevskii Journal of Mathematics, 45 (2024), 1524-1543
4.
M. Turbin, A. Ustiuzhaninova, “Existence of weak solution to initial-boundary value problem for finite order Kelvin-Voigt fluid motion model”, Boletín de la Sociedad Matemática Mexicana, 29 (2023), 54 , 37 pp.
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
6.
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
7.
V. Zvyagin, M. Turbin, “Weak solvability of the initial-boundary value problem for inhomogeneous incompressible Kelvin-Voigt fluid motion model of arbitrary finite order”, Journal of Fixed Point Theory and Applications, 25 (2023), 63 , 41 pp.
V. G. Zvyagin, V. P. Orlov, M. V. Turbin, “Solvability of the initial-boundary value problem for the high-order Oldroyd model”, Russian Math. (Iz. VUZ), 66:7 (2022), 70–75
9.
V. G. Zvyagin, M. V. Turbin, “Existence of attractors for approximations to the Bingham model and their convergence to the attractors of the initial model”, Siberian Math. J., 63:4 (2022), 699–714
10.
M. V. Turbin, A. S. Ustiuzhaninova, “Convergence of attractors for an approximation to attractors of a modified Kelvin–Voigt model”, Comput. Math. Math. Phys., 62:2 (2022), 325–335
11.
M. Turbin, A. Ustiuzhaninova, “Pullback attractors for weak solution to modified Kelvin-Voigt model”, Evolution Equations and Control Theory, 11:6 (2022), 2055–2072
A. Ustiuzhaninova, M. Turbin, “Feedback Control Problem for Modified Kelvin-Voigt Model”, Journal of Dynamical and Control Systems, 28:3 (2022), 465–480
A. S. Ustiuzhaninova, M. V. Turbin, “Trajectory and global attractors for a modified Kelvin—Voigt model”, J. Appl. Industr. Math., 15:1 (2021), 158–168
14.
V. Zvyagin, M. Turbin, “Optimal feedback control problem for inhomogeneous Voigt fluid motion model”, Journal of Fixed Point Theory and Applications, 23 (2021), 4 , 38 pp.
A. Ashyralyev, V. Zvyagin, M. Turbin, “The convergence of approximation attractors to attractors for Bingham model with periodical boundary conditions on spatial variables”, AIP Conference Proceedings, 2325 (2021), 020026 , 6 pp.
16.
V. G. Zvyagin, M. V. Turbin, “The optimal feedback control problem for Voigt model with variable density”, Russian Math. (Iz. VUZ), 64:4 (2020), 80–84
17.
V. Yu. Lyapidevskii, M. V. Turbin, F. F. Khrapchenkov, V. F. Kukarin, “Nonlinear internal waves in multilayer shallow water”, J. Appl. Mech. Tech. Phys., 61:1 (2020), 45–53
18.
M. V. Turbin, A. S. Ustiuzhaninova, “The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions”, Russian Math. (Iz. VUZ), 63:8 (2019), 54–69
19.
P. I. Plotnikov, M. V. Turbin, A. S. Ustiuzhaninova, “Existence Theorem for a Weak Solution of the Optimal Feedback Control Problem for the Modified Kelvin-Voigt Model of Weakly Concentrated Aqueous Polymer Solutions”, Doklady Mathematics, 100:2 (2019), 433–435
20.
V. G. Zvyagin, M. V. Turbin, “Optimal Feedback Control Problem for Bingham Media Motion with Periodic Boundary Conditions”, Doklady Mathematics, 99:2 (2019), 140–142
21.
V. G. Zvyagin, A. V. Zvyagin, M. V. Turbin, “Optimal feedback control problem for the Bingham model with periodical boundary conditions on spatial variables”, Journal of Mathematical Sciences, 244:6 (2020), 959–980
22.
V. G. Zvyagin, M. V. Turbin, “Optimal Feedback Control in the Mathematical Model of Low Concentrated Aqueous Polymer Solutions”, Journal of Optimization Theory and Applications, 148:1 (2011), 146–163
V. G. Zvyagin, M. V. Turbin, “The study of initial-boundary value problems for mathematical models of the motion of Kelvin–Voigt fluids”, Journal of Mathematical Sciences, 168:2 (2010), 157–308
24.
M. V. Turbin, “On the correct formulation of initial-boundary value problems for the generalized Kelvin–Voigt model”, Russian Math. (Iz. VUZ), 50:3 (2006), 47–55
25.
M. V. Turbin, “Research of a mathematical model of low-concentrated aqueous polymer solutions”, Abstract and Applied Analysis, 2006, 012497 , 28 pp.
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