strictly hyperbolic systems of the first order differential equations,
two-dimensional admissible areas boundary problems shift operator functional operator estimation of the spectral radius of the functional operator.
Biography
A.P. Soldatov was born in 1948. He graduated with honors from Novosibirsk State University in 1971 in Mathematics, in 1975 he defended his thesis in the Mathematical Institute of the Academy of Sciences of the USSR n.a. V.A. Steklov, and, in 1981, his doctoral thesis at Moscow State University n.a. M.V. Lomonosov. Since 1984, he holds the academic title of Professor, Honored Scientist of the Russian Federation and a full member of the International Academy of Higher Education since 2001.
A.P. Soldatov is a well-known, actively working specialist in the field of partial differential equations, the author of more than 80 scientific articles and two monographs. In the works of A.P. Soldatov on mixed type equations he investigated a number of well-known boundary-value problems — the generalized Tricomi problem with deviation from the characteristic, the Frankl problem, etc. In particular, he first removed the geometric condition on the elliptical part of the boundary of the domain in the uniqueness theorems for solving the generalized Tricomi problem and Frankl problem. Relatively recently (1994-1995) A.P. Soldatov proposed the new correct statements of mixed problems for the model Lavrentev-Bitsadze equation.
In a large cycle of works by A.P. Soldatov a theory of one-dimensional singular integro-functional operators is built, which are widely used in applications and combine the features of the singular Cauchy operator and Wiener-Hopf operators. These results formed the basis of his monograph “One-dimensional singular operators and boundary value problems of the theory of functions”. A number of important results were obtained by Alexander Pavlovich in the plane theory of elasticity, where he proposed a new method for reducing the basic boundary value problems to an equivalent system of integral equations on the boundary. Applied research by A.P. Soldatov in filtration theory and groundwater level prediction are well-known. He has been successfully cooperating with the Institute of Applied Mathematics and Automation of the Russian Academy of Sciences (Nalchik) for more than ten years in this direction.
In recent years, A.P. Soldatov and his students are actively developing a theoretical-functional approach to general boundary value problems for elliptic equations and systems on a plane, based on the boundary integral equations developed by him. These studies have attracted wide attention of specialists both in our country and abroad. They were presented and discussed at international symposia and congresses such as: International Conference on Operator Theory and Complex Analysis (Mexico City, December 1994); III and VI International Congresses on Industrial and Applied Mathematics (Hamburg, July 1995, Zurich, August 2008); II European Congress of Mathematics (Budapest, July 1996); Congress of the International Society for Analysis, Applications, and Calculations: ISAAC (Delaware, USA, June 1997; Berlin, Germany, July 2001; Ankara, Turkey, 2003). Currently, A.P. Soldatov is the supervisor of six graduate students. Among his students there are 6 candidates and doctors of science. Professor A.P. Soldatov is a member of a number of Russian and international mathematical societies: Moscow Mathematical Society, AMS (USA), GAMM (Germany).
A. P. Soldatov, “Integral representations for second-order elliptic systems in the plane”, Zh. Vychisl. Mat. Mat. Fiz., 64:1 (2024), 129–148; Comput. Math. Math. Phys., 64:1 (2024), 118–137
2023
2.
Sh. A. Alimov, R. R. Ashurov, O. S. Zikirov, B. I. Islomov, T. Sh. Kal'menov, A. P. Soldatov, A. K. Urinov, V. E. Fedorov, T. K. Yuldashev, “Makhmud Salakhitdinovich Salakhitdinov”, Chelyab. Fiz.-Mat. Zh., 8:4 (2023), 463–468
3.
A. P. Soldatov, “Analogue of Kellogg’s theorem for piecewise Lyapunov domains”, Zh. Vychisl. Mat. Mat. Fiz., 63:8 (2023), 1332–1342; Comput. Math. Math. Phys., 63:8 (2023), 1466–1475
A. P. Soldatov, “Singular integral operators with a generalized Cauchy kernel”, Dokl. RAN. Math. Inf. Proc. Upr., 503 (2022), 76–82; Dokl. Math., 105:2 (2022), 117–122
A. P. Soldatov, “Singular integral equations of nonclassical type on a piecewise smooth curve”, Mathematical notes of NEFU, 29:4 (2022), 37–61
6.
A. P. Soldatov, “On a boundary problem for a fourth-order elliptic equation on a plane”, Zh. Vychisl. Mat. Mat. Fiz., 62:4 (2022), 616–624; Comput. Math. Math. Phys., 62:4 (2022), 599–607
2021
7.
B. D. Koshanov, A. P. Soldatov, “On the solvability of the generalized Neumann problem for a higher-order elliptic equation in an infinite domain”, CMFD, 67:3 (2021), 564–575
8.
A. P. Soldatov, O. V. Chernova, “Linear conjugation problem for elliptic systems in the plane”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 195 (2021), 108–117
9.
A. P. Soldatov, “Singular integral operators with generalized Cauchy kernel on piecewise smooth contour”, Mathematical notes of NEFU, 28:3 (2021), 70–84
A. P. Soldatov, “On the Pompeiu integral and its generalizations”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 14:1 (2021), 60–74
11.
M. Otelbaev, A. P. Soldatov, “Integral representations of vector functions based on the parametrix of first-order elliptic systems”, Zh. Vychisl. Mat. Mat. Fiz., 61:6 (2021), 967–976; Comput. Math. Math. Phys., 61:6 (2021), 964–973
L. A. Kovaleva, A. P. Soldatov, “Dirichlet problems for functions that are harmonic on a two-dimensional net”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 160 (2019), 42–48
15.
G. N. Aver'yanov, A. P. Soldatov, “Linear conjugation problem with a triangular matrix coefficient”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 160 (2019), 3–8; J. Math. Sci. (N. Y.), 257:1 (2021), 1–7
A. P. Soldatov, O. V. Chernova, “Riemann–Hilbert Problem for First-Order Elliptic Systems with Constant Leading Coefficients on the Plane”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 149 (2018), 95–102; J. Math. Sci. (N. Y.), 250:5 (2020), 811–818
N. A. Zhura, A. P. Soldatov, “A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain”, Izv. RAN. Ser. Mat., 81:3 (2017), 83–108; Izv. Math., 81:3 (2017), 542–567
A. P. Soldatov, “A boundary value problem for higher order elliptic equations in many connected domain on the plane”, Vladikavkaz. Mat. Zh., 19:3 (2017), 51–58
A. P. Soldatov, Tran Quang Vuong, “The linear conjugation problem for bianalytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 12, 76–81; Russian Math. (Iz. VUZ), 60:12 (2016), 62–66
L. A. Kovaleva, A. P. Soldatov, “The Dirichlet problem on two-dimensional stratified sets”, Izv. RAN. Ser. Mat., 79:1 (2015), 77–114; Izv. Math., 79:1 (2015), 74–108
G. N. Aver'yanov, A. P. Soldatov, “Linear conjugation problem for analytic functions in the weighted Hölder spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 9, 56–61; Russian Math. (Iz. VUZ), 59:9 (2015), 47–50
N. A. Zhura, A. P. Soldatov, “On asymptotics of a piecewise analytic function satisfying contact conditions”, Sibirsk. Mat. Zh., 53:5 (2012), 1001–1006; Siberian Math. J., 53:5 (2012), 800–804
A. P. Soldatov, “On Dirichlet-type problems for the Lavrent'ev–Bitsadze equation”, Trudy Mat. Inst. Steklova, 278 (2012), 242–249; Proc. Steklov Inst. Math., 278 (2012), 233–240
A. P. Soldatov, “Effective boundary conditions for electrodynamic problems with
near-surface sources”, Dokl. Akad. Nauk, 413:5 (2007), 620–623
2006
30.
A. P. Soldatov, “On the index of the Dirichlet problem for elliptic systems on the plane”, Differ. Uravn., 42:8 (2006), 1092–1105; Differ. Equ., 42:8 (2006), 1156–1169
31.
A. P. Soldatov, “Second-order elliptic systems in the half-plane”, Izv. RAN. Ser. Mat., 70:6 (2006), 161–192; Izv. Math., 70:6 (2006), 1233–1264
A. P. Soldatov, “The Bitsadze–Samarskii Problem for Douglis Analytic Functions”, Differ. Uravn., 41:3 (2005), 396–407; Differ. Equ., 41:3 (2005), 416–428
A. P. Soldatov, “On the First and Second Boundary Value Problems for Elliptic Systems on the Plane”, Differ. Uravn., 39:5 (2003), 674–686; Differ. Equ., 39:5 (2003), 712–725
A. P. Soldatov, “Riemann–Hilbert Problems for the Lavrent'ev–Bitsadze System in a Mixed Domain with a Characteristic
Part of the Boundary”, Differ. Uravn., 38:12 (2002), 1653–1663; Differ. Equ., 38:12 (2002), 1753–1763
A. P. Soldatov, “Problem $R$ for the Lavrent'ev–Bitsadze System in Weighted Hardy Classes”, Differ. Uravn., 38:10 (2002), 1418–1430; Differ. Equ., 38:10 (2002), 1510–1523
A. P. Soldatov, “The Algebra of Singular Operators with Terminal Symbol on a Piecewise Smooth Curve: III. Operators of Normal Type”, Differ. Uravn., 37:10 (2001), 1364–1376; Differ. Equ., 37:10 (2001), 1435–1448
A. P. Soldatov, “The Algebra of Singular Operators with Terminal Symbol on a Piecewise Smooth Curve: II. Basic Constructions”, Differ. Uravn., 37:6 (2001), 825–838; Differ. Equ., 37:6 (2001), 866–879
A. P. Soldatov, “The algebra of singular operators with terminal symbol on a piecewise smooth curve: I. Convolution type operators on a semiaxis”, Differ. Uravn., 36:9 (2000), 1209–1219; Differ. Equ., 36:9 (2000), 1337–1347
A. P. Soldatov, “The Riemann–Hilbert problem for the Lavrent'ev–Bitsadze system”, Differ. Uravn., 34:12 (1998), 1649–1659; Differ. Equ., 34:12 (1998), 1656–1666
1997
43.
A. P. Soldatov, S. P. Mitin, “On a class of strongly elliptic systems”, Differ. Uravn., 33:8 (1997), 1118–1122; Differ. Equ., 33:8 (1997), 1125–1129
S. P. Mitin, A. P. Soldatov, “On the solvability of the generalized mixed problem”, Differ. Uravn., 32:3 (1996), 384–388; Differ. Equ., 32:3 (1996), 388–392
1994
45.
A. P. Soldatov, “Dirichlet-type problems for the Lavrent'ev–Bitsadze equation”, Differ. Uravn., 30:11 (1994), 2001–2009; Differ. Equ., 30:11 (1994), 1846–1853
A. P. Soldatov, “Dirichlet-type problems for the Lavrent'ev–Bitsadze equation. II. Existence theorems”, Dokl. Akad. Nauk, 333:1 (1993), 16–18; Dokl. Math., 48:3 (1994), 433–437
A. P. Soldatov, “Dirichlet-type problems for the Lavrent'ev–Bitsadze equation. I. Uniqueness theorems”, Dokl. Akad. Nauk, 332:6 (1993), 696–698; Dokl. Math., 48:2 (1994), 410–414
S. P. Mitin, A. P. Soldatov, “On the solvability of mixed-contact problems in two-dimensional elasticity theory”, Differ. Uravn., 29:5 (1993), 885–889; Differ. Equ., 29:5 (1993), 760–763
1992
50.
A. P. Soldatov, “On a Carleman-type problem for elliptic systems”, Differ. Uravn., 28:1 (1992), 143–151; Differ. Equ., 28:1 (1992), 136–144
51.
A. P. Soldatov, “A function theorety method in elliptic problems in the plane. II. The piecewise smooth case”, Izv. RAN. Ser. Mat., 56:3 (1992), 566–604; Russian Acad. Sci. Izv. Math., 40:3 (1993), 529–563
A. P. Soldatov, “A mixed-contact boundary value problem for elliptic systems”, Differ. Uravn., 27:2 (1991), 279–287; Differ. Equ., 27:2 (1991), 200–207
53.
A. V. Aleksandrov, A. P. Soldatov, “Boundary properties of integrals of Cauchy type. The $L_p$ case”, Differ. Uravn., 27:1 (1991), 3–8; Differ. Equ., 27:1 (1991), 1–5
A. P. Soldatov, “A function theory method in boundary value problems in the plane. I. The smooth case”, Izv. Akad. Nauk SSSR Ser. Mat., 55:5 (1991), 1070–1100; Math. USSR-Izv., 39:2 (1992), 1033–1061
A. P. Soldatov, “Asymptotic behavior of solutions of boundary value problems for
elliptic systems near corner points”, Dokl. Akad. Nauk SSSR, 315:1 (1990), 34–36; Dokl. Math., 42:3 (1991), 725–727
A. P. Soldatov, “A general boundary value problem for elliptic systems”, Dokl. Akad. Nauk SSSR, 311:3 (1990), 539–543; Dokl. Math., 41:2 (1990), 282–286
A. P. Soldatov, “A general boundary value problem of $(k-1)$st order for elliptic
equations”, Dokl. Akad. Nauk SSSR, 311:1 (1990), 39–43; Dokl. Math., 41:2 (1990), 222–226
N. A. Zhura, A. P. Soldatov, “A mixed-contact problem in the plane theory of elasticity in domains with a piecewise smooth boundary”, Differ. Uravn., 24:1 (1988), 55–64; Differ. Equ., 24:1 (1988), 42–50
1987
64.
A. P. Soldatov, M. H. Shhanukov, “Boundary value problems with A. A. Samarskii general nonlocal condition for higher-order pseudoparabolic equations”, Dokl. Akad. Nauk SSSR, 297:3 (1987), 547–552; Dokl. Math., 36:3 (1988), 507–511
A. P. Soldatov, “The algebra of $\mathscr{B}$ singular operators”, Dokl. Akad. Nauk SSSR, 282:6 (1985), 1312–1316
1982
69.
A. P. Soldatov, “On a Riemann–Hilbert problem with a shift”, Dokl. Akad. Nauk SSSR, 266:2 (1982), 291–294
70.
A. P. Soldatov, “On a class of singular integral operators on the line with one-sided shift”, Differ. Uravn., 18:1 (1982), 127–131
1981
71.
A. P. Soldatov, “Algebra of singular integral operators with shift-contraction on the half line”, Differ. Uravn., 17:1 (1981), 137–149
1980
72.
A. P. Soldatov, “A problem of linear conjunction with a shift on a piecewise smooth line in weighted spaces”, Dokl. Akad. Nauk SSSR, 253:5 (1980), 1050–1055
73.
A. P. Soldatov, “Singular operators with a shift on a piecewise smooth line in weighted spaces”, Dokl. Akad. Nauk SSSR, 252:3 (1980), 555–559
74.
A. P. Soldatov, “Singular integral operators on the line”, Differ. Uravn., 16:1 (1980), 135–144
A. P. Soldatov, “A boundary value problem of linear conjugation in the theory of functions”, Izv. Akad. Nauk SSSR Ser. Mat., 43:1 (1979), 184–202; Math. USSR-Izv., 14:1 (1980), 175–192
A. P. Soldatov, “On the Noether theory of singular operators of general form”, Dokl. Akad. Nauk SSSR, 238:5 (1978), 1067–1070
80.
A. P. Soldatov, “On the Noether theory of operators”, Dokl. Akad. Nauk SSSR, 238:2 (1978), 281–284
81.
A. P. Soldatov, “On the Noether theory of operators. One-dimensional singular integral operators of classical type”, Differ. Uravn., 14:7 (1978), 1285–1295
82.
A. P. Soldatov, “On the Noether theory of operators. One-dimensional singular integral operators of general form”, Differ. Uravn., 14:4 (1978), 706–718
A. P. Soldatov, “The uniqueness of the solution of a certain problem of A. V. Bicadze”, Differ. Uravn., 8:1 (1972), 143–146
2024
89.
A. Ya. Belov, V. M. Buchstaber, V. B. Vasilyev, Yu. P. Virchenko, S. K. Kuizheva, A. G. Kusraev, D. K. Mamyi, A. B. Muravnik, A. V. Pskhu, S. A. Rozanova, Z. A. Saidov, A. L. Semenov, S. M. Sitnik, A. L. Skubachevskii, A. P. Soldatov, E. L. Shishkina, A. G. Yagola, “Sultan Nazhmudinovich Askhabov (on the 70-th anniversary of his birth)”, Chebyshevskii Sb., 25:2 (2024), 5–19
2021
90.
A. I. Aptekarev, D. E. Apushkinskaya, O. V. Besov, V. I. Burenkov, V. V. Vlasov, R. V. Gamkrelidze, M. L. Gol'dman, G. V. Demidenko, V. G. Zadorozhniy, V. V. Kozlov, G. G. Lazareva, S. P. Novikov, V. M. Savchin, V. A. Sadovnichii, A. L. Skubachevskii, A. P. Soldatov, D. V. Treschev, M. A. Ragusa, H.-O. Walther, “Vladimir Mikhailovich Filippov”, CMFD, 67:3 (2021), 423–426
A. V. Abanin, O. G. Avsyankin, V. I. Burenkov, B. G. Vakulov, S. K. Vodopyanov, M. L. Gol'dman, V. S. Guliev, I. M. Erusalimskyi, A. N. Karapetyants, M. I. Karyakin, V. M. Kokilashvili, A. G. Kusraev, E. R. Liflyand, A. V. Pskhu, V. S. Rabinovich, S. V. Rogozin, B. S. Rubin, A. P. Soldatov, I. M. Spitkovsky, V. D. Stepanov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Stefan Grigorievich Samko (on the occasion of his 80th birthday)”, Vladikavkaz. Mat. Zh., 23:3 (2021), 126–129
92.
N. L. Abasheieva, S. A. Zagrebina, A. A. Zamyshlyaeva, A. V. Keller, A. I. Kozhanov, G. A. Sviridyuk, S. I. Kabanikhin, E. I. Safonov, A. P. Soldatov, V. V. Slavskii, “Sergey Grigorievich Pyatkov
(on 65th birthday)”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 14:1 (2021), 131–133
2017
93.
A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Alexey Borisovich Shabat (on his 80's anniversary)”, Vladikavkaz. Mat. Zh., 19:3 (2017), 83–85
94.
A. P. Soldatov, A. I. Kozhanov, “On the centenary of the birth of A. V. Bitsadze”, Sib. J. Pure and Appl. Math., 17:3 (2017), 3–7
2012
95.
A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Shabat Aleksei Borisovich (on his 75th birthday)”, Vladikavkaz. Mat. Zh., 14:2 (2012), 71–73
96.
I. E. Egorov, S. I. Kabanikhin, T. Sh. Kal'menov, A. V. Keller, Yu. M. Kovalev, E. V. Radkevich, K. B. Sabitov, A. P. Soldatov, “Alexander Kozhanov (to the $60^{th}$ anniversary)”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 14, 187–189
A. A. Andreev, M. T. Dzhenaliev, A. N. Zarubin, A. I. Kozhanov, E. I. Moiseev, A. M. Nakhushev, V. A. Nakhusheva, E. N. Ogorodnikov, A. V. Pskhu, L. S. Pulkina, N. R. Radjabov, V. P. Radchenko, E. V. Radkevich, O. A. Repin, K. B. Sabitov, A. P. Soldatov, “In Memory of Anatoliy A. Kilbas”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 5(21) (2010), 6–9
Задача Римана-Гильберта для эллиптических систем первого порядка A. P. Soldatov VI International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev November 15, 2023 15:20
2.
Integral representations for second-order elliptic systems A. P. Soldatov International Scientific Conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis - 2023 (OTHA-2023)" August 22, 2023 12:10