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Soldatov, Alexandr Pavlovich

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Total publications: 80
Scientific articles: 75
Presentations: 2

Number of views:
This page:5236
Abstract pages:10339
Full texts:4228
References:808
Soldatov, Alexandr Pavlovich
Professor
Doctor of physico-mathematical sciences
E-mail:
Keywords: 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).


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Publications in Math-Net.Ru
2020
1. A. P. Soldatov, “A Factorization Problem on a Smooth Two-Dimensional Surface”, Mat. Zametki, 108:2 (2020),  285–290  mathnet; Math. Notes, 108:2 (2020), 272–276  isi  scopus
2019
2. L. A. Kovaleva, A. P. Soldatov, “Dirichlet problems for functions that are harmonic on a two-dimensional net”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 160 (2019),  42–48  mathnet  mathscinet
3. G. N. Aver'yanov, A. P. Soldatov, “Linear conjugation problem with a triangular matrix coefficient”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 160 (2019),  3–8  mathnet  mathscinet
2018
4. 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. Ser. Sovrem. Mat. Pril. Temat. Obz., 149 (2018),  95–102  mathnet  mathscinet
2017
5. A. P. Soldatov, “Singular integral operators and elliptic boundary-value problems. I”, CMFD, 63:1 (2017),  1–189  mathnet  mathscinet
6. 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  mathnet  mathscinet  elib; Izv. Math., 81:3 (2017), 542–567  isi  scopus
7. 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  mathnet
2016
8. A. P. Soldatov, “On the theory of anisotropic flat elasticity”, CMFD, 60 (2016),  114–163  mathnet
9. A. P. Soldatov, Tran Quang Vuong, “The linear conjugation problem for bianalytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, 12,  76–81  mathnet; Russian Math. (Iz. VUZ), 60:12 (2016), 62–66  isi  scopus
10. A. P. Soldatov, “On the Spectral Radius of Functional Operators”, Mat. Zametki, 100:1 (2016),  155–162  mathnet  mathscinet  elib; Math. Notes, 100:1 (2016), 132–138  isi  scopus
2015
11. L. A. Kovaleva, A. P. Soldatov, “The Dirichlet problem on two-dimensional stratified sets”, Izv. RAN. Ser. Mat., 79:1 (2015),  77–114  mathnet  mathscinet  zmath  elib; Izv. Math., 79:1 (2015), 74–108  isi  scopus
12. G. N. Aver'yanov, A. P. Soldatov, “Linear conjugation problem for analytic functions in the weighted Hölder spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, 9,  56–61  mathnet; Russian Math. (Iz. VUZ), 59:9 (2015), 47–50  scopus
2014
13. A. P. Soldatov, “Generalized potentials of double layer in plane theory of elasticity”, Eurasian Math. J., 5:2 (2014),  78–125  mathnet
2013
14. A. Soldatov, “The Neumann problem for elliptic systems on a plane”, CMFD, 48 (2013),  120–133  mathnet; Journal of Mathematical Sciences, 202:6 (2014), 897–910  scopus
2012
15. N. A. Zhura, A. P. Soldatov, “On asymptotics of a piecewise analytic function satisfying contact conditions”, Sibirsk. Mat. Zh., 53:5 (2012),  1001–1006  mathnet  mathscinet  elib; Siberian Math. J., 53:5 (2012), 800–804  isi  elib  scopus
16. A. P. Soldatov, “On Dirichlet-type problems for the Lavrent'ev–Bitsadze equation”, Tr. Mat. Inst. Steklova, 278 (2012),  242–249  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 278 (2012), 233–240  isi  elib  scopus
2007
17. A. P. Soldatov, “Effective boundary conditions for electrodynamic problems with near-surface sources”, Dokl. Akad. Nauk, 413:5 (2007),  620–623  mathnet  mathscinet
2006
18. A. P. Soldatov, “On the index of the Dirichlet problem for elliptic systems on the plane”, Differ. Uravn., 42:8 (2006),  1092–1105  mathnet  mathscinet; Differ. Equ., 42:8 (2006), 1156–1169
19. A. P. Soldatov, “Second-order elliptic systems in the half-plane”, Izv. RAN. Ser. Mat., 70:6 (2006),  161–192  mathnet  mathscinet  zmath  elib; Izv. Math., 70:6 (2006), 1233–1264  isi  elib  scopus
2005
20. A. P. Soldatov, “The Bitsadze–Samarskii Problem for Douglis Analytic Functions”, Differ. Uravn., 41:3 (2005),  396–407  mathnet  mathscinet; Differ. Equ., 41:3 (2005), 416–428
2003
21. A. P. Soldatov, “On the First and Second Boundary Value Problems for Elliptic Systems on the Plane”, Differ. Uravn., 39:5 (2003),  674–686  mathnet  mathscinet; Differ. Equ., 39:5 (2003), 712–725
2002
22. 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  mathnet  mathscinet; Differ. Equ., 38:12 (2002), 1753–1763
23. A. P. Soldatov, “Problem $R$ for the Lavrent'ev–Bitsadze System in Weighted Hardy Classes”, Differ. Uravn., 38:10 (2002),  1418–1430  mathnet  mathscinet; Differ. Equ., 38:10 (2002), 1510–1523
24. A. P. Soldatov, “Weighted Hardy Classes of Analytic Functions”, Differ. Uravn., 38:6 (2002),  809–817  mathnet  mathscinet; Differ. Equ., 38:6 (2002), 855–864
2001
25. 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  mathnet  mathscinet; Differ. Equ., 37:10 (2001), 1435–1448
26. 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  mathnet  mathscinet; Differ. Equ., 37:6 (2001), 866–879
2000
27. 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  mathnet  mathscinet; Differ. Equ., 36:9 (2000), 1337–1347
28. A. P. Soldatov, “The Lavrent'ev–Bitsadze system: Solutions admitting infinite-order zeros”, Differ. Uravn., 36:8 (2000),  1101–1105  mathnet  mathscinet; Differ. Equ., 36:8 (2000), 1220–1224
1999
29. A. P. Soldatov, “On the index of operators with end symbol”, Izv. RAN. Ser. Mat., 63:4 (1999),  171–206  mathnet  mathscinet  zmath; Izv. Math., 63:4 (1999), 791–825  isi  scopus
1998
30. A. P. Soldatov, “The Riemann–Hilbert problem for the Lavrent'ev–Bitsadze system”, Differ. Uravn., 34:12 (1998),  1649–1659  mathnet  mathscinet; Differ. Equ., 34:12 (1998), 1656–1666
1997
31. A. P. Soldatov, S. P. Mitin, “On a class of strongly elliptic systems”, Differ. Uravn., 33:8 (1997),  1118–1122  mathnet  mathscinet; Differ. Equ., 33:8 (1997), 1125–1129
1996
32. S. P. Mitin, A. P. Soldatov, “On the solvability of the generalized mixed problem”, Differ. Uravn., 32:3 (1996),  384–388  mathnet  mathscinet; Differ. Equ., 32:3 (1996), 388–392
1994
33. A. P. Soldatov, “Dirichlet-type problems for the Lavrent'ev–Bitsadze equation”, Differ. Uravn., 30:11 (1994),  2001–2009  mathnet  mathscinet; Differ. Equ., 30:11 (1994), 1846–1853
1993
34. A. P. Soldatov, “Dirichlet-type problems for the Lavrent'ev–Bitsadze equation. II. Existence theorems”, Dokl. Akad. Nauk, 333:1 (1993),  16–18  mathnet  mathscinet  zmath; Dokl. Math., 48:3 (1994), 433–437
35. A. P. Soldatov, “Dirichlet-type problems for the Lavrent'ev–Bitsadze equation. I. Uniqueness theorems”, Dokl. Akad. Nauk, 332:6 (1993),  696–698  mathnet  mathscinet  zmath; Dokl. Math., 48:2 (1994), 410–414
36. A. P. Soldatov, “A generalized Cauchy type integral and a singular integral in Hölder spaces with a weight”, Dokl. Akad. Nauk, 330:2 (1993),  164–166  mathnet  mathscinet  zmath
37. 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  mathnet  mathscinet; Differ. Equ., 29:5 (1993), 760–763
1992
38. A. P. Soldatov, “On a Carleman-type problem for elliptic systems”, Differ. Uravn., 28:1 (1992),  143–151  mathnet  mathscinet  zmath; Differ. Equ., 28:1 (1992), 136–144
39. 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  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 40:3 (1993), 529–563  isi
1991
40. A. P. Soldatov, “A mixed-contact boundary value problem for elliptic systems”, Differ. Uravn., 27:2 (1991),  279–287  mathnet  mathscinet; Differ. Equ., 27:2 (1991), 200–207
41. A. V. Aleksandrov, A. P. Soldatov, “Boundary properties of integrals of Cauchy type. The $L_p$ case”, Differ. Uravn., 27:1 (1991),  3–8  mathnet  mathscinet; Differ. Equ., 27:1 (1991), 1–5
42. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 39:2 (1992), 1033–1061  isi
1990
43. 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  mathnet  mathscinet  zmath; Dokl. Math., 42:3 (1991), 725–727
44. A. P. Soldatov, “A general boundary value problem for elliptic systems”, Dokl. Akad. Nauk SSSR, 311:3 (1990),  539–543  mathnet  mathscinet  zmath; Dokl. Math., 41:2 (1990), 282–286
45. 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  mathnet  mathscinet  zmath; Dokl. Math., 41:2 (1990), 222–226
46. A. P. Soldatov, “Functional operators with a shift”, Differ. Uravn., 26:12 (1990),  2136–2145  mathnet  mathscinet; Differ. Equ., 26:12 (1990), 1620–1628
47. A. P. Soldatov, “A Riemann contact problem”, Differ. Uravn., 26:10 (1990),  1828–1830  mathnet  mathscinet  zmath
48. A. P. Soldatov, “Boundary properties of Cauchy-type integrals”, Differ. Uravn., 26:1 (1990),  131–136  mathnet  mathscinet; Differ. Equ., 26:1 (1990), 116–120
1989
49. A. P. Soldatov, “Higher-order elliptic systems”, Differ. Uravn., 25:1 (1989),  136–144  mathnet  mathscinet; Differ. Equ., 25:1 (1989), 109–115
1988
50. A. P. Soldatov, “A general boundary value problem of function theory”, Dokl. Akad. Nauk SSSR, 299:4 (1988),  825–828  mathnet  mathscinet  zmath; Dokl. Math., 37:2 (1988), 486–489
51. 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  mathnet  mathscinet; Differ. Equ., 24:1 (1988), 42–50
1987
52. 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  mathnet  mathscinet; Dokl. Math., 36:3 (1988), 507–511
53. A. P. Soldatov, “A mixed problem of the plane theory of elasticity in regions with a piecewise-smooth boundary”, Differ. Uravn., 23:1 (1987),  161–168  mathnet  mathscinet
1986
54. A. P. Soldatov, “An analogue of an integral of Cauchy type for elliptic systems”, Dokl. Akad. Nauk SSSR, 289:4 (1986),  800–804  mathnet  mathscinet  zmath
55. A. P. Soldatov, “Asymptotic behavior of solutions of singular integral equations”, Differ. Uravn., 22:1 (1986),  143–153  mathnet  mathscinet
1985
56. A. P. Soldatov, “The algebra of $\mathscr{B}$ singular operators”, Dokl. Akad. Nauk SSSR, 282:6 (1985),  1312–1316  mathnet  mathscinet  zmath
1982
57. A. P. Soldatov, “On a Riemann–Hilbert problem with a shift”, Dokl. Akad. Nauk SSSR, 266:2 (1982),  291–294  mathnet  mathscinet  zmath
58. A. P. Soldatov, “On a class of singular integral operators on the line with one-sided shift”, Differ. Uravn., 18:1 (1982),  127–131  mathnet  mathscinet
1981
59. A. P. Soldatov, “Algebra of singular integral operators with shift-contraction on the half line”, Differ. Uravn., 17:1 (1981),  137–149  mathnet  mathscinet  zmath
1980
60. 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  mathnet  mathscinet  zmath
61. 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  mathnet  mathscinet  zmath
62. A. P. Soldatov, “Singular integral operators on the line”, Differ. Uravn., 16:1 (1980),  135–144  mathnet  mathscinet  zmath
1979
63. A. P. Soldatov, “On the theory of singular integral operators of classical type”, Differ. Uravn., 15:3 (1979),  529–544  mathnet  mathscinet  zmath
64. A. P. Soldatov, “A duality category in the theory of Noetherian operators”, Differ. Uravn., 15:2 (1979),  303–309  mathnet  mathscinet  zmath
65. A. P. Soldatov, “On the theory of singular operators with a shift”, Differ. Uravn., 15:1 (1979),  116–131  mathnet  mathscinet
66. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 14:1 (1980), 175–192  isi
1978
67. A. P. Soldatov, “On the Noether theory of singular operators of general form”, Dokl. Akad. Nauk SSSR, 238:5 (1978),  1067–1070  mathnet  mathscinet  zmath
68. A. P. Soldatov, “On the Noether theory of operators”, Dokl. Akad. Nauk SSSR, 238:2 (1978),  281–284  mathnet  mathscinet  zmath
69. A. P. Soldatov, “On the Noether theory of operators. One-dimensional singular integral operators of classical type”, Differ. Uravn., 14:7 (1978),  1285–1295  mathnet  mathscinet  zmath
70. A. P. Soldatov, “On the Noether theory of operators. One-dimensional singular integral operators of general form”, Differ. Uravn., 14:4 (1978),  706–718  mathnet  mathscinet  zmath
71. A. P. Soldatov, “On the Noether theory of operators. Wiener imbeddings of $B$-algebras”, Differ. Uravn., 14:1 (1978),  104–115  mathnet  mathscinet  zmath
1977
72. A. P. Soldatov, “On the theory of singular integro-functional operators”, Differ. Uravn., 13:1 (1977),  140–154  mathnet  mathscinet  zmath
1975
73. A. P. Soldatov, “A certain class of singular integral equations with a shift of non-Carleman type”, Differ. Uravn., 11:1 (1975),  137–150  mathnet  mathscinet  zmath
1974
74. A. P. Soldatov, “Solution of a certain boundary value problem with shift in the theory of functions”, Differ. Uravn., 10:1 (1974),  143–152  mathnet  mathscinet  zmath
1973
75. A. P. Soldatov, “A certain problem of the theory of functions”, Differ. Uravn., 9:2 (1973),  325–332  mathnet  mathscinet  zmath
1972
76. A. P. Soldatov, “The uniqueness of the solution of a certain problem of A. V. Bicadze”, Differ. Uravn., 8:1 (1972),  143–146  mathnet  mathscinet  zmath

2017
77. 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  mathnet
78. 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  mathnet
2012
79. 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  mathnet
80. 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, 14,  187–189  mathnet
2010
81. 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  mathnet

Presentations in Math-Net.Ru
1.
A. P. Soldatov
V. I. Smirnov Seminar on Mathematical Physics
October 12, 2020 16:30
2. On the solvability of the Dirichlet problem on two-dimensional stratified sets
A. P. Soldatov
International Conference on Differential Equations and Dynamical Systems
July 6, 2014 09:45

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