Application of the theory of the Riemann–Hilbert boundary-value to electromagnetic diffraction, hydrodynamics, the theory of elasticity and fracture mechanics.
Main publications:
Antipov Y.A., Silvestrov V.V., “Hilbert problem for a multiply connected circular domain and the analysis of the Hall effect in a plate”, Quarterly of Applied Mathematics, 68:3 (2010), 563–590
V. V. Sil'vestrov, Yu. O. Vasilieva, “Problem of a thin rigid inclusion inserted in an interfacial crack in the vicinity of its tip”, Prikl. Mekh. Tekh. Fiz., 56:3 (2015), 190–199; J. Appl. Mech. Tech. Phys., 56:3 (2015), 510–518
2011
2.
V. V. Sil'vestrov, A. V. Smirnov, “Elastic stresses in a plane with a thin piecewise-homogeneous inclusion”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(23) (2011), 83–88
3.
Yu. O. Vasilieva, V. V. Sil'vestrov, “Concentrated force acting near the tip of an interface crack with a rigid overlay on its side”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 191–195
2010
4.
E. V. Mochalov, V. V. Sil'vestrov, “Кусочно-однородное тело с жесткими прямолинейными межфазными включениями в случае отслоения части включений от тела”, Matem. Mod. Kraev. Zadachi, 1 (2010), 219–222
5.
Yu. O. Vasilieva, V. V. Sil'vestrov, “Задача о жесткой накладке, расположенной на берегу трещины между разными материалами”, Matem. Mod. Kraev. Zadachi, 1 (2010), 95–98
2006
6.
V. V. Sil'vestrov, A. V. Smirnov, “Пара упругих кольцевых пластин, соединенных вдоль граничных окружностей”, Matem. Mod. Kraev. Zadachi, 1 (2006), 199–201
2004
7.
V. V. Sil'vestrov, “The method of Riemann surfaces in the problem of interface cracks and inclusions under concentrated forces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2004, no. 7, 78–91; Russian Math. (Iz. VUZ), 48:7 (2004), 75–88
V. V. Sil'vestrov, A. Yu. Zemlyanova, “Repair of a plate with a circular hole by applying a patch”, Prikl. Mekh. Tekh. Fiz., 45:4 (2004), 176–183; J. Appl. Mech. Tech. Phys., 45:4 (2004), 605–611
V. V. Sil'vestrov, I. A. Ivanov, “A packet of elastic plates joined along a periodic system of segments”, Prikl. Mekh. Tekh. Fiz., 42:4 (2001), 197–202; J. Appl. Mech. Tech. Phys., 42:4 (2001), 731–736
1992
10.
V. V. Sil'vestrov, “Boundary value problems in the theory of elasticity for a plane with a countable set of cuts”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, no. 4, 61–69; Russian Math. (Iz. VUZ), 36:4 (1992), 60–68
1990
11.
V. V. Sil'vestrov, “Fundamental problems in elasticity theory on a multi-sheeted Riemann surface”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, no. 2, 89–92; Soviet Math. (Iz. VUZ), 34:2 (1990), 108–111
V. V. Sil'vestrov, “Unsteady motion of a system of circular cylinders of variable radii in an ideal incompressible fluid”, Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 1, 70–72; Soviet Math. (Iz. VUZ), 31:1 (1987), 98–100
1982
13.
V. V. Sil'vestrov, “On a solution in closed form of a complete singular integral equation”, Trudy Sem. Kraev. Zadacham, 18 (1982), 193–200
1980
14.
V. V. Sil'vestrov, “The Hilbert boundary value problem for an infinitely connected domain in the class of automorphic functions”, Trudy Sem. Kraev. Zadacham, 17 (1980), 180–194
L. I. Chibrikova, V. V. Sil'vestrov, “Calculation of the genus and the Weierstrass points of a fundamental polygon of a functional group”, Izv. Vyssh. Uchebn. Zaved. Mat., 1979, no. 12, 51–56; Soviet Math. (Iz. VUZ), 23:12 (1979), 53–59
L. I. Chibrikova, V. V. Sil'vestrov, “A construction of an automorphic analogue of the Cauchy kernel for a class of proper discontinuous groups”, Trudy Sem. Kraev. Zadacham, 16 (1979), 202–217
1978
17.
L. I. Chibrikova, V. V. Sil'vestrov, “On the question of the effectiveness of the solution of Riemann's boundary value problem for automorphic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1978, no. 12, 117–121; Soviet Math. (Iz. VUZ), 22:12 (1978), 85–88
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