Serovaĭskiĭ, Semen Yakovlevich

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Total publications: 46
Scientific articles: 46

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Doctor of physico-mathematical sciences (1995)
Speciality: 01.01.03 (Mathematical physics)
Birth date: 22.08.1954
Keywords: nonlinear functional analysis; optimal control theory; partial differential equations; mathematical physics; mathematical simulation; distributions theory; computer technologies.


The conception of extended operator derivative is proved. The exemples of non-differentiable operators with extended derivative are bringing. The theorem of extended differentiability of inverse function is proved. It is indicate, that differential dependence of the resolution of the boundary problem for a nonlinear partial equation to avaible component is progressively degraded with the augmentation of nonlinearity coefficient and set dimension; it is depend also to point of differentiation. The necessary conditions of optimality fot the nonlinear infinite dimensional systems without differentiability of system state to the control are accepted. The conception of the sequential model and sequential state for the mathematical physic problems are proposed. It is indicate, that the creation of mathematical model, quality analysis of the system and basing of numerical method of resolution are realized together with use of sequential method. It is exhibited the binding of sequential state and rhe generalized resolution of the mathematicsl physics problem. The sequential extention of optimal control problem is proposed.


Graduated from Faculty of Mechaniks and Applead Mathematics of Kazakh National University in 1976 (department of applead mathematics). Ph.D. thesis was defended in 1983. D.Sci. thesis was defended in 1994. A list of my works contains more than 150 totles, including 5 monographs.

Main publications:
  • Serovajsky S. Arithmetical Distributions and the Sequential Extension of Binary Relations // Mathematical notes, v. 65, no. 6, 1999, 705–717.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. S. Ya. Serovaĭskiĭ, “Optimal Control of Singular Stationary Systems with Phase Constraints and State Variation”, Mat. Zametki, 97:5 (2015),  761–766  mathnet  mathscinet  elib; Math. Notes, 97:5 (2015), 774–778  isi  scopus
2. S. Ya. Serovaiskii, “An optimal control problem for a nonlinear elliptic equation with a phase constraint and state variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, 9,  81–86  mathnet; Russian Math. (Iz. VUZ), 57:9 (2013), 67–70  scopus
3. S. Ya. Serovaĭskiĭ, “Approximation Methods in Optimal Control Problems for Nonlinear Infinite-Dimensional Systems”, Mat. Zametki, 94:4 (2013),  600–619  mathnet  mathscinet  zmath  elib; Math. Notes, 94:4 (2013), 567–582  isi  elib  scopus
4. S. Ya. Serovaĭskiĭ, “Optimal Control of Nonlinear Evolution Systems in the Case where the Solution is not Differentiable with Respect to the Control”, Mat. Zametki, 93:4 (2013),  586–603  mathnet  mathscinet  zmath  elib; Math. Notes, 93:4 (2013), 593–606  isi  elib  scopus
5. A. A. Ashimov, As. A. Ashimov, Yu. V. Borovskii, D. A. Novikov, S. Ya. Serovaiskii, B. T. Sultanov, “Elements of the theory and methods of parametric regulation of national economy's evolution using discrete dynamic stochastic models”, Avtomat. i Telemekh., 2012, 7,  55–66  mathnet; Autom. Remote Control, 73:7 (2012), 1156–1164  isi  scopus
6. S. Ya. Serovaiskii, “The necessary optimality conditions for a nonlinear stationary system whose state functional is not differentiable with respect to the control”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, 6,  32–46  mathnet  mathscinet  elib; Russian Math. (Iz. VUZ), 54:6 (2010), 26–38  scopus
7. S. Ya. Serovaiskii, “Differentiation of operators and optimality conditions in category interpretation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, 2,  66–76  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 54:2 (2010), 57–65  scopus
8. S. Ya. Serovaĭskiĭ, “Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a solution of the boundary-value problem”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, 1,  76–83  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 53:1 (2009), 64–70
9. S. Ya. Serovaĭskiĭ, “Sequential differentiation and its applications in optimal control problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, 7,  45–56  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 52:7 (2008), 38–47
10. S. Ya. Serovaĭskiĭ, “Sequential differentiation in nonsmooth infinite-dimensional extremal problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, 1,  48–62  mathnet  mathscinet; Russian Math. (Iz. VUZ), 52:1 (2008), 45–58
11. S. Ya. Serovaĭskiĭ, “Sequential derivatives of operators and their applications in nonsmooth problems of optimal control”, Izv. Vyssh. Uchebn. Zaved. Mat., 2006, 12,  75–87  mathnet  mathscinet; Russian Math. (Iz. VUZ), 50:12 (2006), 73–84
12. S. Ya. Serovaĭskiĭ, “Optimal control in nonlinear infinite-dimensional systems with nondifferentiability of two types”, Mat. Zametki, 80:6 (2006),  885–901  mathnet  mathscinet  zmath  elib; Math. Notes, 80:6 (2006), 833–847  isi  scopus
13. S. Ya. Serovaĭskiĭ, “A control problem in coefficients and an extended derivative with respect to a convex set”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, 12,  46–55  mathnet  mathscinet  elib; Russian Math. (Iz. VUZ), 49:12 (2005), 43–51
14. S. Ya. Serovaĭskiĭ, “Optimal control for a singular equation with a nonsmooth operator and an isoperimetric condition”, Izv. Vyssh. Uchebn. Zaved. Mat., 2004, 12,  58–65  mathnet  mathscinet; Russian Math. (Iz. VUZ), 48:12 (2004), 55–62
15. S. Ya. Serovaĭskiĭ, “An approximate solution of an optimal control problem for a singular equation of elliptic type with a nonsmooth nonlinearity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2004, 1,  80–86  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 48:1 (2004), 77–83
16. S. Ya. Serovaĭskiĭ, “Approximate Penalty Method in Optimal Control Problems for Nonsmooth Singular Systems”, Mat. Zametki, 76:6 (2004),  893–904  mathnet  mathscinet  zmath; Math. Notes, 76:6 (2004), 834–843  isi  scopus
17. S. Ya. Serovaĭskiĭ, “Optimal Control of an Elliptic Equation with a Nonsmooth Nonlinearity”, Differ. Uravn., 39:10 (2003),  1420–1424  mathnet  mathscinet; Differ. Equ., 39:10 (2003), 1497–1502
18. S. Ya. Serovaĭskiĭ, “Lower augmentation and extension of extremal problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2003, 5,  30–41  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 47:5 (2003), 28–38
19. S. Ya. Serovaĭskiĭ, “Approximate Solution of Singular Optimization Problems”, Mat. Zametki, 74:5 (2003),  728–738  mathnet  mathscinet  zmath; Math. Notes, 74:5 (2003), 685–694  isi
20. S. Ya. Serovaĭskiĭ, “Approximate solution of optimization problems for infinite-dimensional singular systems”, Sibirsk. Mat. Zh., 44:3 (2003),  660–673  mathnet  mathscinet  zmath; Siberian Math. J., 44:3 (2003), 519–528  isi
21. S. Ya. Serovaĭskiĭ, “Arithmetic distributions and sequential extension of binary relations”, Mat. Zametki, 65:6 (1999),  836–853  mathnet  mathscinet  zmath; Math. Notes, 65:6 (1999), 705–717  isi
22. S. Ya. Serovaĭskiĭ, “Optimal control of a nonlinear singular system with a fixed terminal state”, Differ. Uravn., 33:8 (1997),  1114–1117  mathnet  mathscinet; Differ. Equ., 33:8 (1997), 1121–1124
23. S. Ya. Serovaĭskiĭ, “Extendedly differentiable manifolds”, Izv. Vyssh. Uchebn. Zaved. Mat., 1997, 1,  56–65  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 41:1 (1997), 53–62
24. S. Ya. Serovaĭskiĭ, “Extremal problems on differentiable submanifolds of a Banach space”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, 5,  83–86  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:5 (1996), 81–84
25. S. Ya. Serovaĭskiĭ, “On a minimax problem for nonlinear elliptic equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, 4,  66–74  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:4 (1996), 64–72
26. S. Ya. Serovaĭskiĭ, “Optimal control of a nonlinear singular system with state constraints”, Mat. Zametki, 60:4 (1996),  511–518  mathnet  mathscinet  zmath; Math. Notes, 60:4 (1996), 383–388  isi
27. S. Ya. Serovaĭskiĭ, “Gradient methods in an optimal control problem for a nonlinear elliptic system”, Sibirsk. Mat. Zh., 37:5 (1996),  1154–1166  mathnet  mathscinet  zmath; Siberian Math. J., 37:5 (1996), 1016–1027  isi
28. S. Ya. Serovaĭskiĭ, “Necessary conditions for an extremum in the case of the nondifferentiability of the state function with respect to the control”, Differ. Uravn., 31:6 (1995),  1055–1059  mathnet  mathscinet; Differ. Equ., 31:6 (1995), 987–991
29. S. Ya. Serovaĭskiĭ, “An inverse mapping theorem and extended differentiability in Banach spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, 8,  39–49  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 39:8 (1995), 37–46
30. S. Ya. Serovaĭskiĭ, “Optimization in a nonlinear parabolic system with a control in the coefficients”, Mat. Sb., 185:4 (1994),  151–160  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 81:2 (1995), 533–543  isi
31. S. Ya. Serovaĭskiĭ, “Differentiation of Inverse Functions in Spaces without Norm”, Funktsional. Anal. i Prilozhen., 27:4 (1993),  84–87  mathnet  mathscinet  zmath; Funct. Anal. Appl., 27:4 (1993), 290–292  isi
32. S. Ya. Serovaĭskiĭ, “Optimization in a nonlinear elliptic system with control in the coefficients”, Mat. Zametki, 54:2 (1993),  85–95  mathnet  mathscinet  zmath; Math. Notes, 54:2 (1993), 825–832  isi
33. S. Ya. Serovaĭskiĭ, “The regularization method in a problem of the optimal control of a nonlinear hyperbolic system”, Differ. Uravn., 28:12 (1992),  2188–2190  mathnet  mathscinet; Differ. Equ., 28:12 (1992), 1834–1836
34. S. Ya. Serovaĭskiĭ, “Optimal control in a nonlinear stationary system with a nonmonotone operator”, Differ. Uravn., 28:9 (1992),  1579–1587  mathnet  mathscinet; Differ. Equ., 28:9 (1992), 1300–1307
35. S. Ya. Serovaĭskiĭ, “Pareto optimality for a system described by a nonlinear equation of parabolic type”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, 11,  55–64  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 36:11 (1992), 53–62
36. S. Ya. Serovaĭskiĭ, “Stability with respect to linear approximation in infinite-dimensional systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, 8,  57–64  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 36:8 (1992), 53–59
37. S. Ya. Serovaĭskiĭ, “Necessary conditions for optimality for a class of nonlinear singular elliptic systems”, Sibirsk. Mat. Zh., 33:2 (1992),  206–210  mathnet  mathscinet  zmath; Siberian Math. J., 33:2 (1992), 359–363  isi
38. S. Ya. Serovaĭskiĭ, “Extended differentiability of an implicit function in spaces without a norm”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, 12,  55–63  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:12 (1991), 56–63
39. S. Ya. Serovaĭskiĭ, “Approximate conditions for optimality for a system described by a nonlinear parabolic equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, 11,  52–60  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:11 (1991), 52–60
40. S. Ya. Serovaĭskiĭ, “Necessary and sufficient conditions for optimality for a system described by a nonlinear elliptic equation”, Sibirsk. Mat. Zh., 32:3 (1991),  141–150  mathnet  mathscinet  zmath; Siberian Math. J., 32:3 (1991), 468–476  isi
41. S. Ya. Serovaĭskiĭ, “Linearizability of infinite-dimensional control systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, 12,  71–80  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 34:12 (1990), 87–98
42. S. Ya. Serovaĭskiĭ, “Quasiconjugate systems and necessary conditions for optimality in nonlinear infinite-dimensional systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1989, 4,  61–69  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 33:4 (1989), 75–84
43. S. Ya. Serovaĭskiĭ, “Method of Tikhonov regularization in a problem of optimal control of a nonlinear parabolic system”, Sibirsk. Mat. Zh., 30:1 (1989),  212–215  mathnet  mathscinet  zmath; Siberian Math. J., 30:1 (1989), 163–165  isi
44. A. T. Lukyanov, S. Ya. Serovaĭskiĭ, “The method of successive approximations in the problem of optimal control of a nonlinear parabolic system”, Zh. Vychisl. Mat. Mat. Fiz., 24:11 (1984),  1638–1648  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 24:6 (1984), 23–30
45. A. T. Lukyanov, S. Ya. Serovaĭskiĭ, “Optimal control for a bilinear hyperbolic system”, Izv. Vyssh. Uchebn. Zaved. Mat., 1983, 10,  46–48  mathnet  mathscinet
46. S. Ya. Serovaĭskiĭ, “A control problem in coefficients for equations of parabolic type”, Izv. Vyssh. Uchebn. Zaved. Mat., 1982, 12,  44–50  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 26:12 (1982), 45–52

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