01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
3.07.1948
E-mail:
,
Main publications:
V. G. Zvyagin, N. M. Ratiner, Topologicheskie metody v teorii nelineinykh fredgolmovykh otobrazhenii i ikh prilozheniya, Nauka, Moskva, 2019 , 543 pp.
V. G. Zvyagin, S. V. Kornev, Metod napravlyayuschikh funktsii i ego modifikatsii, URSS, Moskva, 2018 , 168 pp.
V. G. Zvyagin, Vvedenie v topologicheskie metody nelineinogo analiza, Izdatelskii dom VGU, Voronezh, 2014 , 291 pp.
V. G. Zvyagin, M. V. Turbin, Matematicheskie voprosy gidrodinamiki vyazkouprugikh sred, URSS, Moskva, 2012 , 416 pp.
V. G. Zvyagin, S. K. Kondratev, Attraktory dlya uravnenii modelei dvizheniya vyazkouprugikh sred, Izdatelsko-poligraficheskii tsentr Voronezhskogo gosudarstvennogo universiteta, Voronezh, 2010 , 266 pp.
V. G. Zvyagin, D. A. Vorotnikov, Topological approximation methods for evolutionary problems of nonlinear hydrodynamics, De Gruyter Series in Nonlinear Analysis and Applications, 12, Walter de Gruyter & Co., Berlin, 2008 , 230 pp.
V. G. Zvyagin, V. T. Dmitrienko, Approksimatsionno-topologicheskii podkhod k issledovaniyu zadach gidrodinamiki. Sistema Nave-Stoksa, Editorial URSS, Moskva, 2004 , 112 pp.
V. G. Zvyagin, V. P. Orlov, “On weak solvability of fractional models of viscoelastic high order fluid”, Izv. Math., 88:1 (2024), 54–76
2.
A. V. Zvyagin, V. G. Zvyagin, V. P. Orlov, “Some properties of trajectories of a nonhomogeneous velocity field of a viscoelastic fluid in a multiconnected domain”, Math. Notes, 116:4 (2024), 853–857
3.
A. V. Borovskikh, V. G. Zadorozhnii, A. V. Zvyagin, V. G. Zvyagin, V. G. Kurbatov, V. V. Obukhovskii, “K devyanostoletiyu Anatoliya Ivanovicha Perova”, Differentsialnye uravneniya, 60:1 (2024), 143-144
4.
V. Zvyagin, V. Orlov, A. Zvyagin, “On some properties of trajectories of non-smooth vector fields”, Mathematics, 12:11 (2024), 1703 , 18 pp.
5.
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, 45:4 (2024), 1524–1543
6.
V. G. Zvyagin, Teoriya topologicheskoi stepeni otobrazhenii konechnomernykh prostranstv i ee prilozheniya, Lan, Sankt-Peterburg, 2024 , 108 pp.
2023
7.
V. G. Zvyagin, V. P. Orlov, “The weak solvability of an inhomogeneous dynamic problem
for a viscoelastic continuum with memory”, Funct. Anal. Appl., 57:1 (2023), 74–79
8.
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
9.
V. G. Zvyagin, V. P. Orlov, “The problem of the flow of one type of non-Newtonian fluid through the boundary of a multi-connected domain”, Dokl. Math., 107:2 (2023), 112–116
10.
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
11.
V. G. Zvyagin, A. S. Ustiuzhaninova, “Pullback attractors of the Bingham model”, Differential Equations, 59:3 (2023), 377-382
12.
V. G. Zvyagin, E. I. Kostenko, “Investigation of the weak solvability of one fractional model with infinite memory”, Lobachevskii Journal of Mathematics, 44:3 (2023), 969–988
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, “On weak solvability of a flow problem for viscoelastic fluid with memory”, Computational Mathematics and Mathematical Physics, 63:11 (2023), 2090–2106
2022
15.
V. G. Zvyagin, V. P. Orlov, “Weak solvability of motion models for a viscoelastic fluid with a higher-order rheological relation”, Russian Math. Surveys, 77:4 (2022), 753–755
16.
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
17.
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
2021
18.
V. G. Zvyagin, V. P. Orlov, “On strong solutions of fractional nonlinear viscoelastic model of Voigt type”, Mathematical Methods in the Applied Sciences, 44 (2021), 11768–11782
V. Zvyagin, M. Turbin, “Optimal feedback control problem for inhomogeneous Voigt fluid motion model”, Journal of Fixed Point Theory and Applications, 23:4 (2021)
V. G. Zvyagin, V. P. Orlov, “Weak Solvability of One Viscoelastic Fractional Dynamics Model of Continuum with Memory”, Journal of Mathematical Fluid Mechanics, 23:9 (2021)
V. G. Zvyagin, A. V. Zvyagin, N. M. Hong, “Optimal Feedback Control for a Model of Motion of a Nonlinearly Viscous Fluid”, Differential Equations, 57:1 (2021), 122–126
22.
M. Ashyraliyev, A. Ashyralyev, V. Zvyagin, “On the source identification problem for hyperbolic-parabolic equation with nonlocal conditions”, AIP Conference Proceedings, 2325 (2021), 020016 , 4 pp.
23.
A. Ashyralyev, C. Ashyralyyev, V. G. Zvyagin, “On well-posedness of source identification elliptic problem with nonlocal boundary conditions”, AIP Conference Proceedings, 2325 (2021), 020021 , 3 pp.
24.
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.
25.
A. Ashyralyev, V. Zvyagin, A. Zvyagin, “About optimal feedback control problem for motion model of nonlinearly viscous fluid”, AIP Conference Proceedings, 2325 (2021), 020003 , 4 pp.
26.
V. G. Zvyagin, V. P. Orlov, “On a priori estimates of weak solutions of one nongomogeneous problem of dynamics of viscoelastic medium with memory”, Russian Mathematics, 65:5 (2021), 30–39
27.
V. G. Zvyagin, V. P. Orlov, “Strong solutions of one model of dynamics of thermoviscoelasticity of a continuous medium with memory”, Russian Mathematics, 65:6 (2021), 84–89
28.
V. G. Zvyagin, V. V. Obukhovskii, “Yurii Grigorevich Borisovich”, Izvestiya vuzov. Matematika, 2021, no. 5, 3–5
29.
A. S. Arsentev, E. G. Belomyttseva, V. G. Zvyagin, V. P. Orlov, “O resheniyakh nachalno-kraevoi zadachi dlya modeli Dzheffrisa-Oldroida i odnoi integrodifferentsialnoi sistemy”, Vestnik VGU. Seriya: Fizika. Matematika, 2021, no. 1, 59–72
30.
V. G. Zvyagin, M. V. Kaznacheev, “Attractors for an autonomous model of the motion of a nonlinear viscous fluid”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 191, VINITI, Moscow, 2021, 74–91
31.
A. Boldyrev, V. Zvyagin, “Attractors for Weak Solutions of a Regularized Model of Viscoelastic Mediums Motion with Memory in Non-autonomous Case”, Springer Proceedings in Mathematics and Statistics, 351 (2021), 3–27
32.
A. V. Zvyagin, V. G. Zvyagin, “Weak solvability of termo-Voigt-α model”, Lobachevskii Journal of Mathematics, 42:15 (2021), 3793–3809
2020
33.
V. G. Zvyagin, M. V. Turbin, “The optimal feedback control problem for Voigt model with variable density”, Russian Mathematics, 64 (2020), 80–84
34.
V. G. Zvyagin, A. V. Zvyagin, N. M. Hong, “Optimal feedback control for one motion model of a nonlinearly viscous fluid”, Chebyshevskii Sbornik, 21:2 (2020), 144-158
35.
V. G. Zvyagin, V. P. Orlov, A. S. Arsentiev, “Equivalence of weak solvability of initial-boundary value problems for the Jeffries-Oldroyd model and one integro-differential system with memory”, Russian Mathematics, 64:6 (2020), 69–74
36.
V. G. Zvyagin, M. V. Kaznacheev, “Attractors of an autonomous model of nonlinear viscous fluid”, Doklady Mathematics, 101:2 (2020), 126–128
37.
V. Zvyagin, A. Zvyagin, A. Ustiuzhaninova, “Optimal feedback control problem for the fractional Voigt-α model”, Mathematics, 8 (2020), 1197 , 27 pp.
A. Ashyralyev, C. Ashyralyyev, V. G. Zvyagin, “A note on well-posedness of source identification elliptic problem in a Banach space”, Bulletin of the Karaganda university. Mathematics series, 99:3 (2020), 96–103
39.
V. G. Zvyagin, V. P. Orlov, “On regularity of weak solutions to a generalized Voigt model of viscoelasticity”, Computational Mathematics and Mathematical Physics, 60:11 (2020), 1872–1888
2019
40.
A. V. Zvyagin, V. G. Zvyagin, D. M. Polyakov, “Dissipative Solvability of an Alpha Model of Fluid Flow with Memory”, Computational Mathematics and Mathematical Physics, 59:7 (2019), 1185–1198
41.
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
42.
A. S. Boldyrev, V. G. Zvyagin, “Attractors for Model of Viscoelastic Media with Memory Motion in Non-Autonomous Case”, Lobachevskii Journal of Mathematics, 40:7 (2019), 918–937
V. G. Zvyagin, N. M. Ratiner, Topologicheskie metody v teorii nelineinykh fredgolmovykh otobrazhenii i ikh prilozheniya, Nauka, Moskva, 2019 , 543 pp.
44.
V. G. Zvyagin, V. P. Orlov, “On strong solutions of a fractional nonlinear viscoelastic Voigt-type model”, Russian Mathematics, 63 (2019), 96–100
2018
45.
V. G. Zvyagin, S. V. Kornev, Metod napravlyayuschikh funktsii i ego modifikatsii, URSS, Moskva, 2018 , 168 pp.
46.
A. V. Zvyagin, V. G. Zvyagin, D. M. Polyakov, “On solvability of one alpha-model of fluid motion with memory”, Russian Math. (Iz. VUZ), 62:6 (2018), 69–74
47.
V. G. Zvyagin, V. P. Orlov, “Solvability of one non-Newtonian fluid dynamics model with memory”, Nonlinear Analysis, 172 (2018), 73–98
A. S. Boldyrev, V. G. Zvyagin, “Attractors for Weak Solutions of a Regularized Model of Viscoelastic Mediums Motion With Memory in Non-Autonomous Case”, Russian Mathematics, 62:7 (2018), 63–67
2019
49.
V. G. Zvyagin, A. V. Zvyagin, “Optimal feedback control for a thermoviscoelastic model of the motion of water polymer solutions”, Siberian Adv. Math., 29:2 (2019), 137–152
2018
50.
V. G. Zvyagin, N. N. Avdeev, “Example of a System Whose Minimal Trajectory Attractor Does not Contain Solutions of the System”, Math. Notes, 104:6 (2018), 922–926
51.
V. G. Zvyagin, V. P. Orlov, “On solvability of an initial-boundary value problem for a viscoelasticity model with fractional derivatives”, Siberian Math. J., 59:6 (2018), 1073–1089
2020
52.
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 (2020), 959–980
2018
53.
V. G. Zvyagin, V. P. Orlov, “Weak solvability of fractional voigt model of viscoelasticity”, Discrete and Continuous Dynamical Systems- Series A, 38:12 (2018), 6327–6350
V. G. Zvyagin, N. M. Ratiner, “Degree of locally condensing perturbations of Fredholm maps with positive index and applications”, Journal of Functional Analysis, 275:10 (2018), 2573–2613
V. G. Zvyagin, V. P. Orlov, “On one problem of viscoelastic fluid dynamics with memory on an infinite time interval”, Discrete and Continuous Dynamical Systems - Series B, 23:9 (2018), 3855–3877
R. S. Adamova, V. G. Zvyagin, “O voronezhskoi matematicheskoi shkole (posvyaschaetsya 100-letiyu Voronezhskogo gosudarstvennogo universiteta)”, Matematika v vysshem obrazovanii, 2018, no. 16, 49–58http://www.unn.ru/math/no/16/_nom16_007_Adamova.pdf
57.
V. M. Kuz’kin, S. A. Pereselkov, V. G. Zvyagin, A. Yu. Malykhin, D. Yu. Prosovetskiy, “Intense Internal Waves and Their Manifestation in Interference Patterns of Received Signals on Oceanic Shelf”, Physics of Wave Phenomena, 26:2 (2018), 160–167
V. G. Zvyagin, V. P. Orlov, “On the Weak Solvability of a Fractional Viscoelasticity Model”, Doklady Mathematics, 98:3 (2018), 568-570
2017
59.
V. G. Zvyagin, V. P. Orlov, “On problem of the dynamics of a viscoelastic medium with memory on an infinite interval”, Doklady Mathematics, 96:1 (2017), 329–331
60.
A. V. Zvyagin, V. G. Zvyagin, “Pullback attractors for a model of weakly concentrated aqueous polymer solution motion with a rheological relation satisfying the objectivity principle”, Doklady Mathematics, 95:3 (2017), 247–249
61.
V. G. Zvyagin, V. P. Orlov, “Weak solvability of a fractional Voigt viscoelasticity model”, Doklady Mathematics, 96:2 (2017), 491–493
62.
V. G. Zvyagin, V. P. Orlov, “On the weak solvability of the problem of viscoelasticity with memory”, Differential Equations, 53:2 (2017), 212–217
63.
V. G. Zvyagin, V. P. Orlov, “Solvability of a parabolic problem with non-smooth data”, Journal of Mathematical Analysis and Applications, 453:1 (2017), 589–606
V. G. Zvyagin, “Attractors theory for autonomous systems of hydrodynamics and its application to Bingham model of fluid motion”, Lobachevskii Journal of Mathematics, 38:4 (2017), 767–777
V. G. Zvyagin, S. V. Kornev, “Existence of an attractor for three-dimensional model of the Bingham fluid motion”, Russian Math. (Iz. VUZ), 60:1 (2016), 64–67
66.
V. G. Zvyagin, V. P. Orlov, “On the Parabolic Problem of Motion of Thermoviscoelastic Media”, Math. Notes, 99:3 (2016), 465–469
67.
V. G. Zvyagin, V. P. Orlov, “On a model of thermoviscoelasticity of Jeffreys–Oldroyd type”, Comput. Math. Math. Phys., 56:10 (2016), 1803–1812
68.
V. G. Zvyagin, V. P. Orlov, “Weak solvability of irregularized model of viscoelastisity with memory”, AIP Conference Proceedings, 1759 (2016), 020040 , 7 pp.
69.
V. G. Zvyagin, V. P. Orlov, “On a Weak Solvability of a System of Thermoviscoelasticity of Oldroyd’s Type”, Differential and Difference Equations with Applications, 164, Springer Proceedings in Mathematics & Statistics, 2016, 401–409
70.
V. G. Zvyagin, S. K. Kondratyev, “Pullback attractors of the Jeffreys–Oldroyd equations”, Journal of Differential Equations, 260:6 (2016), 5026–5042
V. G. Zvyagin, A. V. Zvyagin, “Pullback attractors for a model of polymer solutions motion with rheological relation satisfying the objectivity principle”, Journal of Mathematical Sciences, 248 (2020), 600–620
2018
72.
V. G. Zvyagin, S. V. Kornev, “Method of guiding functions for existence problems for periodic solutions of differential equations”, Journal of Mathematical Sciences, 233:4 (2018), 578–601
2017
73.
V. G. Zvyagin, “The degree of compact multivalued perturbations of Fredholm mappings of positive index and its application to a certain optimal control problem”, J. Math. Sci., 223:6 (2017), 695–710
2015
74.
V. G. Zvyagin, S. K. Kondrat'ev, “Pullback attractors for the model of motion of dilute aqueous polymer solutions”, Izv. Math., 79:4 (2015), 645–667
75.
V. G. Zvyagin, V. P. Orlov, “On the weak solvability of one system of thermoviscoelasticity”, AIP Conference Proceedings, 1676 (2015), 020011 , 6 pp.
76.
V. G. Zvyagin, V. V. Obukhovskii, A. V. Zvyagin, “On inclusions with multivalued operators and their applications to some optimization problems”, Journal of Fixed Point Theory and Applications, 16:1-2 (2015), 27–82
V. G. Zvyagin, S. K. Kondrat'ev, “Attractors of equations of non-Newtonian fluid dynamics”, Russian Math. Surveys, 69:5 (2014), 845–913
78.
V. G. Zvyagin, Vvedenie v topologicheskie metody nelineinogo analiza, Izdatelskii dom VGU, Voronezh, 2014 , 291 pp.
79.
V. G. Zvyagin, “Topological Approximation Approach to Study of Mathematical Problems of Hydrodynamics”, Journal of Mathematical Sciences, 201:6 (2014), 830–858
V. G. Zvyagin, V. P. Orlov, “On certain mathematical models in continuum thermomechanics”, Journal of Fixed Point Theory and Applications, 15:1 (2014), 3–47
V. G. Zvyagin, “Ob orientirovannoi stepeni mnogoznachnykh vozmuschenii fredgolmovykh otobrazhenii polozhitelnogo indeksa”, Doklady Akademii Nauk, 457:4 (2014), 388–390
82.
V. G. Zvyagin, S. K. Kondratyev, “Pullback attractors for a model of motion of weak aqueous polymer solutions”, Doklady Mathematics, 90:3 (2014), 660–662
83.
V, P. Orlov, M. I. Parshin, V. G. Zvyagin, “On strong solutions for a Navier-Stokes-Fourier-Oldroid system”, Contemporary Analysis and Applied Mathematics, 2:2 (2014), 277–289
2013
84.
V. G. Zvyagin, V. P. Orlov, “Weak solvability of a system of thermoviscoelasticity for Jeffris model”, Russian Math. (Iz. VUZ), 57:9 (2013), 53–57
85.
V. G. Zvyagin, S. K. Kondratyev, “Approximating topological approach to the existence of attractors in fluid mechanics”, Journal of Fixed Point Theory and Applications, 13:2 (2013), 359–395
V. G. Zvyagin, “Topological approximation approach to study of mathematical problems of hydrodynamics”, Journal of Mathematical Sciences, 201:6 (2014), 830–858
2015
87.
V. G. Zvyagin, N. M. Ratiner, “Oriented degree of Fredholm maps: finite-dimensional reduction method”, Journal of Mathematical Sciences, 204:5 (2015), 543–714
2012
88.
V. G. Zvyagin, S. K. Kondrat'ev, “Attractors of weak solutions to the regularized system of equations of motion of fluid media with memory”, Sb. Math., 203:11 (2012), 1611–1630
89.
V. G. Zvyagin, M. V. Turbin, Matematicheskie voprosy gidrodinamiki vyazkouprugikh sred, URSS, Moskva, 2012 , 416 pp.
2011
90.
V. G. Zvyagin, S. K. Kondrat'ev, “Attractors of weak solutions to a regularized system of motion equations for fluids with memory”, Russian Math. (Iz. VUZ), 55:8 (2011), 75–77
91.
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, E. S. Baranovskii, “Topological degree of condensing multi-valued perturbations of the $(S)_+$-class maps and its applications”, Journal of Mathematical Sciences, 170:3 (2010), 405–422
93.
V. G. Zvyagin, S. K. Kondratev, Attraktory dlya uravnenii modelei dvizheniya vyazkouprugikh sred, Izdatelsko-poligraficheskii tsentr Voronezhskogo gosudarstvennogo universiteta, Voronezh, 2010 , 266 pp.
94.
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
2009
95.
V. G. Zvyagin, A. V. Kuznetsov, “Optimal control in a model of the motion of a viscoelastic medium with objective derivative”, Russian Math. (Iz. VUZ), 53:5 (2009), 48–53
96.
B. M. Darinskii, D. A. Vorotnikov, V G. Zvyagin, “Longitudinal normals and the existence of acoustic axes in crystals”, Nonlinear Analysis: Real World Applications, 10:2 (2009), 798–809
V. G. Zvyagin, A. V. Kuznetsov, “The density of the set of right-hand sides of the initial-boundary value problem for the Jeffreys model of a viscoelastic fluid”, Russian Math. Surveys, 63:6 (2008), 1159–1161
98.
V. G. Zvyagin, D. A. Vorotnikov, Topological approximation methods for evolutionary problems of nonlinear hydrodynamics, De Gruyter Series in Nonlinear Analysis and Applications, 12, Walter de Gruyter & Co., Berlin, 2008 , 230 pp.
D. A. Vorotnikov, V. G. Zvyagin, “Trajectory and global attractors of the boundary value problem for autonomous motion equations of viscoelastic medium”, Journal of Mathematical Fluid Mechanics, 10:1 (2008), 19–44
V. G. Zvyagin, M. Y. Kuzmin, “On an optimal control problem in the Voigt model of the motion of a viscoelastic fluid”, Journal of Mathematical Sciences, 149:5 (2008), 1618–1627
V. G. Zvyagin, D. A. Vorotnikov, “Approximating-topological methods in some problems of hydrodynamics”, Journal of Fixed Point Theory and Applications, 3:1 (2008), 23–49
N. M. Bliznyakov, V. M. Buchstaber, Yu. E. Gliklikh, V. G. Zvyagin, A. S. Mishchenko, V. V. Obukhovskii, Yu. I. Sapronov, A. T. Fomenko, A. V. Chernavskii, “Yurii Grigor'evich Borisovich (obituary)”, Russian Math. Surveys, 63:4 (2008), 767–769
2007
103.
D. A. Vorotnikov, V. G. Zvyagin, “Uniform attractors for non-autonomous motion equations of viscoelastic medium”, Journal of Mathematical Analysis and Applications, 325:1 (2007), 438–458
D. A. Vorotnikov, V. G. Zvyagin, “On the convergence of solutions of the regularized problem for motion equations of Jeffreys viscoelastic medium to solutions of the original problem”, Journal of Mathematical Sciences, 144:5 (2007), 4398–4408
C. Gori, V. V. Obukhovskii, P. Rubbioni, V. G. Zvyagin, “Optimization of the motion of a visco-elastic fluid via multivalued topological degree method”, Dynamic Systems and Applications, 16:1 (2007), 89–104
2008
107.
V. G. Zvyagin, M. Yu. Kuz'min, “On some optimal control problem in the Voigt model of the motion of a viscoelastic fluid”, Journal of Mathematical Sciences, 149:5 (2008), 1618–1627
2006
108.
D. A. Vorotnikov, V. G. Zvyagin, “On the trajectory and global attractors for the equations of motion of a visco-elastic medium”, Russian Math. Surveys, 61:2 (2006), 368–370
109.
D. A. Vorotnikov, B. M. Darinskii, V. G. Zvyagin, “Topological approach to investigation of acoustic axes in crystals”, Crystallography Reports, 51:1 (2006), 104–109
110.
P. Zecca, V. G. Zvyagin, V. V. Obukhovskii, “On oriented coincidence index for nonlinear Fredholm inclusions”, Doklady Mathematics, 73:1 (2006), 63–66
111.
V. V. Obukhovskii, P. Zecca, V. G. Zvyagin, “An oriented index for nonlinear Fredholm inclusions”, Abstract and Applied Analysis, 2006 (2006), 51794 , 21 pp.
R. H. W. Hoppe, M. Y. Kuzmin, W. G. Litvinov, V. G. Zvyagin, “Flow of electrorheological fluid under conditions of slip on the boundary”, Abstract and Applied Analysis, 2006 (2006), 43560 , 14 pp.
V. G. Zvyagin, Yu. E. Gliklikh, V. V. Obukhovskii, “Topological and variational methods of nonlinear analysis and their applications”, Abstract and Applied Analysis, 2006 (2006), 93926 , 2 pp.
2007
115.
D. A. Vorotnikov, V. G. Zvyagin, “On the convergence of solutions of regularized problem for motion equations of Jeffreys viscoelastic medium to solutions of the original problem”, J. Math. Sci., 144:5 (2007), 4398–4408
2005
116.
V. G. Zvyagin, V. P. Orlov, “On weak solutions of the equations of motion of a viscoelastic medium with variable boundary”, Boundary Value Problems, 2005:3 (2005), 215–245
V. T. Dmitrienko, V. G. Zvyagin, “On strong solutions of an initial-boundary value problem for a regularized model of an incompressible viscoelastic medium”, Russian Math. (Iz. VUZ), 48:9 (2004), 21–37
118.
V. G. Zvyagin, V. T. Dmitrienko, Approksimatsionno-topologicheskii podkhod k issledovaniyu zadach gidrodinamiki. Sistema Nave-Stoksa, Editorial URSS, Moskva, 2004 , 112 pp.
119.
V. G. Zvyagin, “On Solvability of Some Initial-Boundary Problems for Mathematical Models of the Motion of Nonlinearly Viscous and Viscoelastic Fluids”, Journal of Mathematical Sciences, 124:5 (2004), 5321–5334
V. V. Obukhovskiǐ, P. Zecca, V. G. Zvyagin, “Optimal feedback control in the problem of the motion of a viscoelastic fluid”, Topological Methods of Nonlinear Analysis, 23:2 (2004), 323–337
D. A. Vorotnikov, V. G. Zvyagin, “On the existence of weak solutions for the initial-boundary value problem in the Jeffreys model of motion of a viscoelastic medium”, Abstract and Applied Analysis, 2004:10 (2004), 815–829
D. A. Vorotnikov, V. G. Zvyagin, “On the solvability of the initial-value problem for the motion equations of nonlinear viscoelastic medium in the whole space”, Nonlinear Analysis: Theory, Methods & Applications, 58:5-6 (2004), 631–656
V. G. Zvyagin, “On Solvability of Some Initial-Boundary Problems for Mathematical Models of the Motion of Nonlinearly Viscous and Viscoelastic Fluids”, Journal of Mathematical Sciences, 124:5 (2004), 5321–5334
2003
124.
V. T. Dmitrienko, M. Kirane, V. G. Zvyagin, “On weak solutions for generalized Oldroyd model for laminar and turbulent flows of nonlinear viscous-elastic fluid”, Nonlinear Analysis. Theory, Methods & Applications, 53:2 (2003), 197–226
V. T. Dmitrienko, V. G. Zvyagin, “Index of solution set for perturbed Fredholm equations and existence of periodic solutions for delay differential equations”, Topological Methods in Nonlinear Analysis, 21:1 (2003), 53–80
2002
126.
V. G. Zvyagin, V. T. Dmitrienko, “On Weak Solutions of a Regularized Model of a Viscoelastic Fluid”, Differ. Equ., 38:12 (2002), 1731–1744
127.
V. V. Obukhovskii, P. Zecca, V. G. Zvyagin, “On coincidence index for multivalued perturbations of nonlinear Fredholm maps and some applications”, Abstract and Applied Analysis, 7:6 (2002), 295–322
V. G. Zvyagin, V. T. Dmitrienko, Z. Kukharski, “Topological characterization of the solution set of Fredholm equations with $f$-compactly contractive perturbations and its applications”, Russian Math. (Iz. VUZ), 45:1 (2001), 33–45
129.
V. T. Dmitrienko, V. G. Zvyagin, “Solvability of the Boundary-Value Problem for a Mathematical Model of Steady-State Flows of Nonlinear-Viscous Fluids”, Math. Notes, 69:6 (2001), 770–779
130.
V. G. Zvyagin, V. T. Dmitrienko, “On Weak Solutions to the Initial Boundary Value Problem for the Motion Equation of a Viscoelastic Fluid”, Doklady Mathematics, 64:2 (2001), 190–193
2000
131.
V. T. Dmitrienko, V. G. Zvyagin, “Indeks mnozhestva reshenii fredgolmovykh uravnenii s f-uplotnyayuschimi vozmuscheniyami i razreshimost periodicheskikh kraevykh zadach”, Izvestiya RAEN, seriya MMMIU, 4:1-2 (2000), 109–143http://www.tvp.ru/ourizd/mmmic_an.htm#vol4
1999
132.
V. G. Zvyagin, V. T. Dmitrienko, “On weak solutions for some model of motion of nonlinear viscous-elastic fluid”, Topological Methods in Nonlinear Analysis, 14:2 (1999), 295–325
133.
V. G. Zvyagin, “Toward a degree theory of equivariant Φ0C1CC-mappings”, Doklady Mathematics, 59:1 (1999), 24–26
134.
V. G. Zvyagin, “K teorii stepeni ekvivariantnykh F0S1VN-otobrazhenii”, Doklady Akademii Nauk, 364:2 (1999), 155–157
V. G. Zvyagin, “The set of critical values of a potential Fredholm functional”, Math. Notes, 63:1 (1998), 118–120
1997
136.
V. G. Zvyagin, “The zero point index of a completely continuous perturbation of a Fredholm mapping that commutes with the action of a torus”, Russian Math. (Iz. VUZ), 41:1 (1997), 43–50
137.
V. T. Dmitrienko, V. G. Zvyagin, “The topological degree method for equations of the Navier-Stokes type”, Abstract and Applied Analysis, 2:1-2 (1997), 1–45
Yu. G. Borisovich, V. G. Zvyagin, V. V. Shabunin, “On the solvability in $W^{2m+l}_p$ of the nonlinear Dirichlet problem in a narrow strip”, Dokl. Math., 49:1 (1994), 179–182
1992
139.
V. G. Zvyagin, N. M. Ratiner, “Oriented degree of Fredholm maps of non-negative index and its application to global bifurcation of solutions”, Lecture Notes in Mathematics, 1520, Springer-Verlag, 1992, 111–137
V. G. Zvyagin, V. T. Dmitrienko, “Properness of nonlinear elliptic differential operators in Hölder spaces”, Lecture Notes in Mathematics, 1520, Springer-Verlag, 1992, 261–284
1991
141.
V. G. Zvyagin, “Number of solutions of the Dirichlet problem for equations elliptic on a set of solutions”, Math. Notes, 49:4 (1991), 365–369
1993
142.
V. G. Zvyagin, “On the oriented degree of a certain class of perturbations of Fredholm mappings, and on bifurcation of solutions of a nonlinear boundary value problem with noncompact perturbations”, Math. USSR-Sb., 74:2 (1993), 487–512
1990
143.
V. G. Zvyagin, “The degree of Fredholm maps equivariant with respect to the actions of the circle and the torus”, Russian Math. Surveys, 45:2 (1990), 229–230
144.
V. G. Zvyagin, “On the structure of the set of solutions of a non-linear elliptic problem with fixed boundary conditions”, Lecture Notes in Mathematics, 1453, Springer-Verlag, 1990, 309–320
V. G. Zvyagin, M. A. Krasnosel'skii, A. S. Mishchenko, Yu. I. Sapronov, V. I. Sobolev, “Yurii Grigor'evich Borisovich (on his sixtieth birthday)”, Russian Math. Surveys, 45:4 (1990), 243–245
1988
147.
V. G. Zvyagin, “On the number of solutions for certain boundary-value problems”, Lecture Notes in Mathematics, 1334, Springer-Verlag, 1988, 157–172
V. G. Zvyagin, “On the theory of generalized condensing perturbations of continuous mappings”, Lecture Notes in Mathematics, 1108, Springer-Verlag, 1984, 173–193
V. T. Dmitrienko, V. G. Zvyagin, “Homotopy classification of a class of continuous mappings”, Math. Notes, 31:5 (1982), 404–410
1979
150.
Yu. G. Borisovich, P. Menz, V. G. Zvyagin, “Nichtlineare FREDHOLM-Operatoren, Abbildungsgrad und Anwendungen auf nichtlineare Eigenwertprobleme”, Mathematische Nachrichten, 91:1 (1979), 281–295
V. G. Zvyagin, “The existence of a continuous branch for the eigenfunctions of a nonlinear elliptic boundary value problem”, Differ. Uravn., 13:8 (1977), 1524–1527
152.
Yu. G. Borisovich, V. G. Zvyagin, Yu. I. Sapronov, “Non-linear Fredholm maps and the Leray–Schauder theory”, Russian Math. Surveys, 32:4 (1977), 1–54
1973
153.
V. G. Zvyagin, È. M. Muhamadiev, Yu. I. Sapronov, “The degree of equivariant Fredholm maps”, Uspekhi Mat. Nauk, 28:6(174) (1973), 209–210
2024
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