An axiomatic description of the Cauchy matrix (kernel of the integral representations of solutions) is given, the adjoint boundary value problem to the general linear boundary value problem is constructed, a method of the study of nonlinear boundary value problems for the solvability with the use of a priori inequality is developed. Jointly with N. V. Azbelev and L. F. Rakhmatullina, the basics of the general theory of functional differential equations are worked out. In colloboration with A. N. Rumyantsev, the constructive methods for the study of boundary value problems, including impulsive ones, are developed with the use of reliable computations; the theory and the imlementation of the reliable computing experiment are worked out, which are aimed to the study of wide classes of problems including some problems in economic dynamics.
Biography
Graduated from the Izhevsk Mechanical Institute in 1970 (department of computer science). Ph.D. thesis was defended in 1974. D.Sci. thesis was defended in 1985. A list of my works contains more than 90 titles including 4 books (with coauthors). Since 1985 I, N. V. Azbelev, and L. F. Rakhmatullina have led the research seminar at the Perm State Technical University on functional differential equations.
In 1994 I was selected by the G. Soros International Scientific Fund as a George Soros professor. Since 1996 I am a member of the Academy of Nonlinear Sciences.
Main publications:
Azbelev N. V., Maksimov V. P., and Rakhmatullina L. F. Introduction to the theory of linear functional differential equations. Atlanta: World Federation Publ., 1995.
Maksimov V. P., Rumyantsev A. N. The study of the solvability of boundary value problems for functional differential equations // Boundary Value Problems for Functional Differential Equations / ed. by J. Henderson. Singapore: World Scientific, 1995, 227–237.
V. P. Maksimov, “On the error of calculating the attainable values of objective functionals for control systems with continuous and discrete times”, Trudy Inst. Mat. i Mekh. UrO RAN, 30:3 (2024), 207–216
2023
2.
V. P. Maksimov, “To probabilistic description of an ensemble of trajectories to a continuous-discrete control system with incomplete information”, Russian Universities Reports. Mathematics, 28:143 (2023), 256–267
2021
3.
V. P. Maksimov, “On internal estimates of reachable sets for continuous-discrete systems with discrete memory”, Trudy Inst. Mat. i Mekh. UrO RAN, 27:3 (2021), 141–151
V. P. Maksimov, “О построении программных управлений в задаче о достижимых значениях целевых функционалов для динамических моделей экономики с дискретной памятью”, Appl. Math. Control Sci., 2020, no. 3, 89–104
6.
V. P. Maksimov, “To estimating linear functionals values over solutions of systems with aftereffect”, Russian Universities Reports. Mathematics, 25:131 (2020), 274–283
7.
V. P. Maksimov, “On a class of linear continuous-discrete systems with discrete memory”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:3 (2020), 385–395
V. P. Maksimov, “On the construction and estimates of the Cauchy matrix for systems with aftereffect”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:3 (2019), 153–162
V. P. Maksimov, “The structure of the Cauchy operator to a linear continuous-discrete functional differential system with aftereffect and some properties of its components”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:1 (2019), 40–51
V. P. Maksimov, “On a class of optimal control problems for functional differential systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:1 (2018), 131–142; Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S114–S124
V. P. Maksimov, “Attainable values of on-target functionals for a functional differential system with impulses”, Tambov University Reports. Series: Natural and Technical Sciences, 23:123 (2018), 441–447
V. P. Maksimov, “Reliable computing experiment in the study of functional-differential equations: theory and applications”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132 (2017), 64–67; J. Math. Sci. (N. Y.), 230:5 (2018), 712–716
V. P. Maksimov, “On guaranteed estimate of reconstruction error of parameters of linear difference system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 10, 72–76; Russian Math. (Iz. VUZ), 59:10 (2015), 61–64
2013
15.
V. P. Maksimov, “Control of functional differential system in conditions of impulse disturbances”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 9, 70–74; Russian Math. (Iz. VUZ), 57:9 (2013), 58–61
V. P. Maksimov, “Functional differential continuous-discrete systems”, Izv. IMI UdGU, 2012, no. 1(39), 88–89
17.
V. P. Maksimov, A. L. Chadov, “A class of controls for a functional-differential continuous-discrete system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 9, 72–76; Russian Math. (Iz. VUZ), 56:9 (2012), 62–65
V. P. Maksimov, A. L. Chadov, “The constructive investigation of boundary-value problems with approximate satisfaction of boundary conditions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 10, 82–86; Russian Math. (Iz. VUZ), 54:10 (2010), 71–74
N. V. Azbelev, V. P. Maksimov, P. M. Simonov, “Functional differential equations and their applications”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, no. 1, 3–23
A. D. Andrianov, V. P. Maksimov, P. M. Simonov, “Краевые задачи для разностных моделей”, Matem. Mod. Kraev. Zadachi, 3 (2008), 20–23
21.
V. P. Maksimov, P. M. Simonov, “Functional differential equations and their applications”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 2, 87–90
2006
22.
V. P. Maksimov, “Problems of impulsive and mixed control for linear functional differential systems”, Izv. IMI UdGU, 2006, no. 3(37), 87–88
V. P. Maksimov, “Control problems for linear functional differential systems. Constructive approach, computer-assisted study, applications”, Izv. IMI UdGU, 2006, no. 2(36), 73–78
2002
24.
V. P. Maksimov, A. N. Rumyantsev, “Convincing computational experiment in the study of functional differential systems”, Izv. IMI UdGU, 2002, no. 2(25), 61–64
1997
25.
V. P. Maksimov, “Some problems of a regularization for overdetermined boundary value problems of economics dynamics”, Matem. Mod., 9:2 (1997), 57–65
V. P. Maksimov, A. N. Rumyantsev, “Boundary value problems and problems of impulse control in economic dynamics. Constructive investigation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, no. 5, 56–71; Russian Math. (Iz. VUZ), 37:5 (1993), 48–62
S. A. Gusarenko, E. S. Zhukovskiy, V. P. Maksimov, “On the theory of functional-differential equations with locally Volterra operators”, Dokl. Akad. Nauk SSSR, 287:2 (1986), 268–272
N. V. Azbelev, V. P. Maksimov, “A priori estimates of the solutions of the Cauchy problem and the solvability of boundary value problems for equations with retarded argument”, Differ. Uravn., 15:10 (1979), 1731–1747
V. P. Maksimov, “The property of being Noetherian of the general boundary value problem for a linear functional differential equation”, Differ. Uravn., 10:12 (1974), 2288–2291
1973
37.
V. P. Maksimov, L. F. Rakhmatullina, “A linear functional-differential equation that is solved with respect to the derivative”, Differ. Uravn., 9:12 (1973), 2231–2240
V. P. Maksimov, L. F. Rakhmatullina, “The representation of the solutions of a linear functional-differential equation”, Differ. Uravn., 9:6 (1973), 1026–1036
N. R. Abubakirov, F. G. Avkhadiev, A. V. Aminova, M. M. Arslanov, A. M. Bikchentaev, V. V. Vasin, F. N. Garif'yanov, A. M. Denisov, A. M. Elizarov, N. K. Zamov, B. A. Kats, O. A. Kashina, D. V. Maklakov, V. P. Maksimov, S. R. Nasyrov, N. I. Popov, L. G. Salekhov, R. B. Salimov, S. G. Samko, N. Temirgaliev, E. A. Turilova, Yu. E. Hohlov, P. L. Shabalin, L. N. Shevrin, A. N. Sherstnev, E. A. Shirokova, V. V. Shurygin, “Leonid Aleksandrovich Aksent'ev”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 3, 98–100
2020
40.
A. V. Arutyunov, M. V. Borzova, E. O. Burlakov, A. A. Grigorenko, E. S. Zhukovskiy, S. E. Zhukovskiy, V. P. Maksimov, E. A. Panasenko, E. A. Pluzhnikova, A. V. Ponosov, V. M. Tikhomirov, O. V. Filippova, I. A. Finogenko, Yu. G. Fomicheva, A. G. Chentsov, A. I. Shindyapin, “In memory of professor Alexander Ivanovich Bulgakov”, Russian Universities Reports. Mathematics, 25:129 (2020), 100–102
2019
41.
A. A. Gryzlov, V. A. Zaitsev, D. M. Kinzebulatov, N. V. Latypova, V. P. Maksimov, N. N. Petrov, S. N. Popova, V. I. Rodionov, L. I. Rodina, Yu. M. Smetanin, D. L. Fedorov, “Vasilii Yakovlevich Derr. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019), 612–617
2002
42.
I. V. Gaishun, N. A. Izobov, V. A. Il'in, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, N. Kh. Rozov, T. K. Shemjakina, “N. V. Azbelev (A tribute on the occasion of his 80th birthday)”, Differ. Uravn., 38:7 (2002), 867–869; Differ. Equ., 38:7 (2002), 917–919
1997
43.
N. A. Izobov, V. A. Il'in, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, T. K. Shemjakina, “Nikolaǐ Viktorovich Azbelev (on the occasion of his seventy-fifth birthday)”, Differ. Uravn., 33:4 (1997), 435–439; Differ. Equ., 33:4 (1997), 433–438
1982
44.
N. P. Erugin, N. A. Izobov, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, “Nikolaǐ Viktorovich Azbelev (on the occasion of his sixtieth birthday)”, Differ. Uravn., 18:4 (1982), 725–730
Presentations in Math-Net.Ru
1.
К оценке значений линейных функционалов на решениях систем с последействием В. П. Максимов International Scientific Conference KOLMOGOROV READINGS – IX. General Control Problems and their Applications (GCP–2020), dedicated to the 70-th birth anniversary of Alexander Ivanovich Bulgakov and to the 90-th anniversary of the Institute of Mathematics, Physics and Information
Technologies of Derzhavin Tambov State University October 13, 2020 11:00
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