Differential equations, control, stability, systems with delays, mathematical modelling.
Main publications:
A. B. Kim, Pryamoi metod Lyapunova v teorii ustoichivosti sistem s posledeistviem, Uralskii gosuniversitet, Ekaterinburg, 1992
A. B. Kim, $i$-Gladkii analiz i funktsionalno-differentsialnye uravneniya, IMM UrO RAN, Ekaterinburg, 1996
A. B. Kim, V. G. Pimenov, $i$-Gladkii analiz i chislennye metody resheniya funktsionalno-differentsialnykh uravnenii, Regulyarnaya i khaoticheskaya dinamika, M.–Izhevsk, 2004
A. B. Kim, Pryamoi metod Lyapunova v teorii ustoichivosti sistem s posledeistviem, Uralskii gosuniversitet, Ekaterinburg, 1992
A. V. Kim, “Introduction to the theory of positional differentional games of systems with aftereffect (based on the $i$-smooth analisys methodology”, Russian Universities Reports. Mathematics, 29:147 (2024), 268–295
2021
2.
A. V. Kim, “On application of the $i$-smooth analysis methodology to elaboration of numerical methods for solving functional differential equations”, Russian Universities Reports. Mathematics, 26:133 (2021), 26–34
A. V. Kim, G. A. Bocharov, “Minimax differential game with delay”, Russian Universities Reports. Mathematics, 25:132 (2020), 359–369
2012
4.
A. A. Belov, A. V. Kim, “Optimal stabilization of the combustion process in liquid rocket motors”, Izv. IMI UdGU, 2012, no. 1(39), 12
2007
5.
A. V. Kim, N. G. Kolmogortseva, “On the degree of smoothness of solutions of functional differential equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 13:2 (2007), 120–123; Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S159–S162
A. Yu. Vdovin, A. V. Kim, S. S. Rubleva, “On asymptotic accuracy in $L_1$ of a dynamical algorithm for reconstructing a disturbance”, Trudy Inst. Mat. i Mekh. UrO RAN, 12:2 (2006), 18–26; Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S216–S224
A. V. Kim, S. S. Rubleva, Y.-S. Choi, “On the problem of analytical construction of regulators for systems with delays”, Trudy Inst. Mat. i Mekh. UrO RAN, 11:1 (2005), 111–121; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 1, S122–S133
A. V. Kim, A. B. Lozhnikov, “A Stability Criterion for Linear Functional-Differential Equations and Its Practical Implementation”, Differ. Uravn., 40:2 (2004), 271–273; Differ. Equ., 40:2 (2004), 290–293
A. V. Kim, A. B. Lozhnikov, “Mathematical modeling of systems with aftereffect: theory, algorithms, software”, Izv. IMI UdGU, 2002, no. 2(25), 55–58
2000
10.
A. V. Kim, A. B. Lozhnikov, “A linear-quadratic problem for systems with delay in the state. Exact solutions of Riccati equations”, Avtomat. i Telemekh., 2000, no. 7, 15–31; Autom. Remote Control, 61:7 (2000), 1076–1090
A. V. Kim, V. G. Pimenov, “Application of $i$-smooth analysis to construction of numerical methods for solving functional-differential equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 5 (1998), 119–142
A. V. Kim, “On first integrals of functional-differential equations”, Differ. Uravn., 33:3 (1997), 347–350; Differ. Equ., 33:3 (1997), 344–347
1991
13.
Yu. F. Dolgii, A. V. Kim, “On the method of Lyapunov functionals for systems with aftereffect”, Differ. Uravn., 27:8 (1991), 1313–1318; Differ. Equ., 27:8 (1991), 918–922
S. L. Grigor'ev, A. V. Kim, A. I. Korotkii, I. A. Tsepelev, “On dynamical modelling of parameters of some thermal processes”, Matem. Mod., 3:8 (1991), 72–81
1990
15.
A. V. Kim, “Method of lyapunov functionals for systems with aftereffect”, Avtomat. i Telemekh., 1990, no. 2, 24–31; Autom. Remote Control, 51:2 (1990), 152–158
A. V. Kim, “On a problem of multiplication of linear functionals and generalized functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1988, no. 6, 69–71; Soviet Math. (Iz. VUZ), 32:6 (1988), 93–97
1987
17.
A. V. Kim, “The solution of nonlinear boundary value problems for ordinary differential equations”, Differ. Uravn., 23:9 (1987), 1504–1510
18.
A. V. Kim, “Generalized solutions of nonlinear differential equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 5, 58–63; Soviet Math. (Iz. VUZ), 31:5 (1987), 76–83
1985
19.
A. V. Kim, “On Lyapunov's second method for systems with aftereffect”, Differ. Uravn., 21:3 (1985), 385–391
HIV process — differential game A. V. Kim, G. А. Bocharov International Conference “Differential Equations and Optimal Control” dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko June 8, 2022 12:50
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