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Danilin, Aleksei Rufimovich
Statistics Math-Net.Ru
Total publications: 58
Scientific articles: 56

Number of views:
This page:3491
Abstract pages:27945
Full texts:6221
References:3695
Professor
Doctor of physico-mathematical sciences
E-mail:

https://www.mathnet.ru/eng/person8634
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/205116
https://elibrary.ru/author_items.asp?spin=9984-3120

Publications in Math-Net.Ru Citations
2025
1. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of a solution to a terminal control problem with two small parameters”, Mat. Sb., 216:8 (2025),  82–111  mathnet  mathscinet; Sb. Math., 216:8 (2025), 1092–1120  isi
2. A. R. Danilin, I. V. Pershin, “Asymptotics of a solution to an optimal boundary control problem with performance index defined on the boundary”, Trudy Inst. Mat. i Mekh. UrO RAN, 31:2 (2025),  94–107  mathnet  elib
2024
3. A. R. Danilin, “Asymptotics of the solution of a bisingular optimal distributed control problem in a convex domain with a small parameter multiplying a highest derivative”, Zh. Vychisl. Mat. Mat. Fiz., 64:5 (2024),  732–744  mathnet  elib; Comput. Math. Math. Phys., 64:5 (2024), 941–953
2023
4. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotic expansion of the solution to an optimal control problem for a linear autonomous system with a terminal convex quality index depending on slow and fast variables”, Izv. IMI UdGU, 61 (2023),  42–56  mathnet 1
5. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:2 (2023),  41–53  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 323, suppl. 1 (2023), S85–S97  scopus
6. A. R. Danilin, A. A. Shaburov, “Asymptotics of a Solution to an Optimal Control Problem with Integral Convex Performance Index, Cheap Control, and Initial Data Perturbations”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:1 (2023),  67–76  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 321, suppl. 1 (2023), S69–S77  isi  scopus
7. A. R. Danilin, “Asymptotics for solutions of problem on optimally distributed control in convex domain with small parameter at one of higher derivatives”, Ufimsk. Mat. Zh., 15:2 (2023),  42–54  mathnet; Ufa Math. J., 15:2 (2023), 42–54 1
2022
8. A. R. Danilin, A. A. Shaburov, “Asymptotic expansion of the solution of a singularly perturbed optimal control problem with elliptical control constraints”, Avtomat. i Telemekh., 2022, no. 1,  3–21  mathnet  mathscinet; Autom. Remote Control, 83:1 (2022), 1–16  isi  scopus
9. A. R. Danilin, A. A. Shaburov, “Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control”, Sib. Zh. Ind. Mat., 25:3 (2022),  5–13  mathnet; J. Appl. Industr. Math., 16:3 (2022), 387–393 2
10. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of a solution to a time-optimal control problem with an unbounded target set in the critical case”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:1 (2022),  58–73  mathnet  mathscinet  elib 5
11. A. R. Danilin, “Asymptotic expansion for the solution of an optimal boundary control problem in a doubly connected domain with different control intensity on boundary segments”, Zh. Vychisl. Mat. Mat. Fiz., 62:2 (2022),  217–231  mathnet  elib; Comput. Math. Math. Phys., 62:2 (2022), 218–231  isi  scopus 1
2021
12. A. R. Danilin, “Asymptotics of a solution to a problem of optimal boundary control with two small cosubordinate parameters. II”, Trudy Inst. Mat. i Mekh. UrO RAN, 27:2 (2021),  108–119  mathnet  elib
13. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time of transferring a linear control system with zero real parts of the eigenvalues of the matrix at the fast variables to an unbounded target set”, Trudy Inst. Mat. i Mekh. UrO RAN, 27:1 (2021),  48–61  mathnet  elib 3
2020
14. A. R. Danilin, A. A. Shaburov, “Asymptotic expansion of a solution of a singularly perturbed optimal control problem with a convex integral quality index, whose terminal part additively depends on slow and fast variables”, Izv. IMI UdGU, 55 (2020),  33–41  mathnet 1
15. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of a Solution to a Singularly Perturbed Time-Optimal Control Problem of Transferring an Object to a Set”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:2 (2020),  132–146  mathnet  elib; Proc. Steklov Inst. Math., 313, suppl. 1 (2021), S40–S53  isi  scopus 1
16. A. R. Danilin, “Asymptotics of a solution to a problem of optimal boundary control with two small cosubordinate parameters”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:1 (2020),  102–111  mathnet  elib 2
2019
17. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the Solution to a Singularly Perturbed Time-Optimal Control Problem with Two Small Parameters”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:2 (2019),  88–101  mathnet  elib; Proc. Steklov Inst. Math., 309, suppl. 1 (2020), S10–S23  isi  scopus 2
18. A. R. Danilin, A. A. Shaburov, “Asymptotic expansion of solution to singularly perturbed optimal control problem with convex integral quality functional with terminal part depending on slow and fast variables”, Ufimsk. Mat. Zh., 11:2 (2019),  83–98  mathnet; Ufa Math. J., 11:2 (2019), 82–96  isi  scopus 3
2018
19. A. R. Danilin, “Asymptotic expansion of a solution to a singular perturbation optimal control problem with a small coercivity coefficient”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:3 (2018),  51–61  mathnet  elib
20. A. R. Danilin, O. O. Kovrizhnykh, “On a singularly perturbed time-optimal control problem with two small parameters”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:2 (2018),  76–92  mathnet  elib; Proc. Steklov Inst. Math., 307, suppl. 1 (2019), S34–S50  isi
21. A. R. Danilin, “Asymptotics of the solution of a bisingular optimal boundary control problem in a bounded domain”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018),  1804–1814  mathnet  elib; Comput. Math. Math. Phys., 58:11 (2018), 1737–1747  isi  scopus 2
2017
22. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of a solution to a singularly perturbed time-optimal control problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:2 (2017),  67–76  mathnet  elib; Proc. Steklov Inst. Math., 303, suppl. 1 (2018), S60–S69  isi 1
23. A. R. Danilin, S. V. Zakharov, O. O. Kovrizhnykh, E. F. Lelikova, I. V. Pershin, O. Yu. Khachay, “The Yekaterinburg heritage of Arlen Mikhailovich Il'in”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:2 (2017),  42–66  mathnet  elib 2
24. A. R. Danilin, “Asymptotics of the solution to the singular problem of optimal distributed control in a convex domain”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:1 (2017),  128–142  mathnet  elib; Proc. Steklov Inst. Math., 300, suppl. 1 (2018), S72–S87  isi  scopus 1
2016
25. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal control problem with a small parameter”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:1 (2016),  61–70  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 297, suppl. 1 (2017), S62–S71  isi  scopus 1
26. A. R. Danilin, “A complete asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with geometric constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:1 (2016),  52–60  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 296, suppl. 1 (2017), S119–S127  isi  scopus
2015
27. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal control problem with a small parameter”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:1 (2015),  71–80  mathnet  mathscinet  elib
2014
28. A. R. Danilin, “Solution asymptotics in a problem of optimal boundary control of a flow through a part of the boundary”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:4 (2014),  116–127  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 292, suppl. 1 (2016), S55–S66  isi  scopus 6
29. A. R. Danilin, “Asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with integral constraint”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:3 (2014),  76–85  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 291, suppl. 1 (2015), S66–S76  isi  scopus 3
30. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal problem with two small parameters”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:1 (2014),  92–99  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 288, suppl. 1 (2015), S46–S53  isi  scopus 3
2013
31. A. R. Danilin, N. S. Korobitsyna, “Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:3 (2013),  104–112  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 285, suppl. 1 (2014), S58–S67  isi  scopus 3
2012
32. A. R. Danilin, A. P. Zorin, “Asymptotics of a solution to an optimal boundary control problem in a bounded domain”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:3 (2012),  75–82  mathnet  elib 2
33. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotic representation of a solution to a singular perturbation linear time-optimal problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:2 (2012),  67–79  mathnet  elib; Proc. Steklov Inst. Math., 281, suppl. 1 (2013), S22–S35  isi  scopus 5
34. A. R. Danilin, “Optimal boundary control in a small concave domain”, Ufimsk. Mat. Zh., 4:2 (2012),  87–100  mathnet 10
2011
35. A. R. Danilin, O. O. Kovrizhnykh, “The dependence of the time-optimal control problem for a linear system of the small parameters”, Vestnik Chelyabinsk. Gos. Univ., 2011, no. 14,  46–60  mathnet 2
2010
36. A. E. El'bert, A. R. Danilin, “Optimized autophasing of solitons”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:2 (2010),  288–296  mathnet  elib 1
37. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a singular perturbation linear problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:1 (2010),  63–75  mathnet  elib; Proc. Steklov Inst. Math., 271, suppl. 1 (2010), S53–S65  isi  scopus 6
2009
38. A. R. Danilin, A. P. Zorin, “Asymptotics of a solution to an optimal boundary control problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:4 (2009),  95–107  mathnet  elib; Proc. Steklov Inst. Math., 269, suppl. 1 (2010), S81–S94  scopus 13
2007
39. A. R. Danilin, Yu. V. Parysheva, “The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case”, Trudy Inst. Mat. i Mekh. UrO RAN, 13:2 (2007),  55–65  mathnet  elib; Proc. Steklov Inst. Math., 259, suppl. 2 (2007), S83–S94 5
2006
40. A. R. Danilin, “Asymptotics of the optimal value of the performance functional for a rapidly stabilizing indirect control in the regular case”, Differ. Uravn., 42:11 (2006),  1473–1480  mathnet  mathscinet; Differ. Equ., 42:11 (2006), 1545–1552 7
41. A. R. Danilin, “Asymptotic behavior of the optimal cost functional for a rapidly stabilizing indirect control in the singular case”, Zh. Vychisl. Mat. Mat. Fiz., 46:12 (2006),  2166–2177  mathnet  mathscinet; Comput. Math. Math. Phys., 46:12 (2006), 2068–2079  scopus 21
2003
42. A. R. Danilin, “Asymptotic behaviour of solutions of a singular elliptic system in a rectangle”, Mat. Sb., 194:1 (2003),  31–60  mathnet  mathscinet  zmath  elib; Sb. Math., 194:1 (2003), 31–61  isi  scopus 6
43. A. R. Danilin, “Approximation of a singularly perturbed elliptic optimal control problem with geometric constraints on the control”, Trudy Inst. Mat. i Mekh. UrO RAN, 9:1 (2003),  71–78  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 2003no. , suppl. 1, S45–S53 1
2000
44. A. R. Danilin, “Approximation of a singularly perturbed elliptic problem of optimal control”, Mat. Sb., 191:10 (2000),  3–12  mathnet  mathscinet  zmath; Sb. Math., 191:10 (2000), 1421–1431  isi  scopus 19
1998
45. A. R. Danilin, A. M. Il'in, “On the structure of the solution of a perturbed optimal-time control problem”, Fundam. Prikl. Mat., 4:3 (1998),  905–926  mathnet  mathscinet  zmath 18
46. A. R. Danilin, “Asymptotic behaviour of bounded controls for a singular elliptic problem in a domain with a small cavity”, Mat. Sb., 189:11 (1998),  27–60  mathnet  mathscinet  zmath; Sb. Math., 189:11 (1998), 1611–1642  isi  scopus 32
1996
47. A. R. Danilin, A. M. Il'in, “Asymptotic behavior of the solution of the time-optimality problem for a linear system under perturbation of initial data”, Dokl. Akad. Nauk, 350:2 (1996),  155–157  mathnet  mathscinet  zmath 7
48. A. R. Danilin, “Regularization of nonlinear control problems under perturbations of constraints”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 8,  34–38  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:8 (1996), 32–36
1994
49. A. R. Danilin, “Regularization of the problem of the control of a dynamical system in a Hilbert space under conditions of uncertainty”, Differ. Uravn., 30:1 (1994),  172–174  mathnet  mathscinet; Differ. Equ., 30:1 (1994), 160–163
1992
50. A. R. Danilin, “Regularization of a control problem with constraints on the state”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, no. 2,  24–28  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 36:2 (1992), 24–28 1
1985
51. A. R. Danilin, “Order-optimal estimates for finite-dimensional approximations of solutions of ill-posed problems”, Zh. Vychisl. Mat. Mat. Fiz., 25:8 (1985),  1123–1130  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 25:4 (1985), 102–106 4
1984
52. A. R. Danilin, V. P. Tanana, “Necessary and sufficient conditions for convergence of approximations of linear ill-posed problems in a Hilbert space”, Zh. Vychisl. Mat. Mat. Fiz., 24:5 (1984),  633–639  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 24:3 (1984), 5–9
1982
53. V. P. Tanana, A. R. Danilin, “Necessary and sufficient conditions for convergence of finite-dimensional approximations of regularized solutions”, Dokl. Akad. Nauk SSSR, 264:5 (1982),  1094–1096  mathnet  mathscinet  zmath
54. A. R. Danilin, “Necessary and sufficient conditions for the convergence of finite-dimensional approximations of the residual method”, Zh. Vychisl. Mat. Mat. Fiz., 22:4 (1982),  994–997  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 22:4 (1982), 231–235
1980
55. A. R. Danilin, “Conditions for convergence of finite-dimensional approximations of the residual method”, Izv. Vyssh. Uchebn. Zaved. Mat., 1980, no. 11,  38–40  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 24:11 (1980), 41–44 2
1976
56. V. P. Tanana, A. R. Danilin, “The optimality of regularizing algorithms in the solution of ill-posed problems”, Differ. Uravn., 12:7 (1976),  1323–1326  mathnet  mathscinet  zmath 8
2025
57. D. I. Borisov, A. R. Danilin, V. Yu. Novokshenov, “Tribute to Arlen Mikhailovich Il'in”, Mat. Sb., 216:8 (2025),  3–4  mathnet  mathscinet; Sb. Math., 216:8 (2025), 1019–1020  isi
2002
58. V. M. Babich, R. R. Gadyl'shin, A. R. Danilin, S. Yu. Dobrokhotov, V. A. Il'in, L. A. Kalyakin, E. F. Mishchenko, V. Yu. Novokshenov, Yu. S. Osipov, M. D. Ramazanov, N. Kh. Rozov, V. A. Sadovnichii, “Arlen Mikhailovich Il'in (A tribute in honor of his 70th birthday)”, Differ. Uravn., 38:8 (2002),  1011–1016  mathnet  mathscinet; Differ. Equ., 38:8 (2002), 1075–1080

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