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Khapaev, Mikhail Mikhailovich

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Total publications: 70
Scientific articles: 69

Number of views:
This page:995
Abstract pages:7175
Full texts:3077
References:277
Professor
Doctor of physico-mathematical sciences
Birth date: 26.03.1934
UDC: 517.9, 517.928, 518.538.13, 519.642, 517.977.5, 517.925

Subject:

Averaging method and it's applications. Generalization of Ljapunov's second method. Сomputational methods in micromagnetic problems. Variational method in optimal control problems.

   
Main publications:
  1. Khapaev M.M., Usrednenie v teorii ustoichivosti: Issledovanie rezonansnykh mnogochastotnykh sistem, Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1986
  2. Khapaev M.M., “Stability investigation in 3-body problem based on hydrodynamic model of planets”, Doklady Akademii Nauk, 231:5 (1976), 1092–1095
  3. Khapaev M.M., Osipov S.G., Ternovskii V.V., “Modelirovanie trekhmernykh periodicheskikh struktur v ferromagnitnykh plenkakh”, Doklady Akademii Nauk, 305:4 (1989), 831–834
  4. Ternovskii V.V., Khapaev M.M., “Direct numerical method for solving optimal control problems”, Doklady Mathematics, 420:40 (2008), 463–466  crossref
  5. Khapaev M.M., “Evolution of planetary orbits”, Soviet Physics. Doklady, 35:5 (1990), 431–433

http://www.mathnet.ru/eng/person18398
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/100990

Publications in Math-Net.Ru
2018
1. V. V. Ternovskii, M. M. Khapaev, T. M. Khapaeva, “Application of the variational method for solving inverse problems of optimal control”, Dokl. Akad. Nauk, 483:4 (2018),  370–373  mathnet  zmath  elib; Dokl. Math., 98:3 (2018), 603–606  isi  scopus
2016
2. M. M. Khapaev, T. M. Khapaeva, “Computation of eigenfunctions and eigenvalues for the Sturm–Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016),  1750–1753  mathnet  elib; Comput. Math. Math. Phys., 56:10 (2016), 1732–1736  isi  scopus
2015
3. V. V. Ternovski, M. M. Khapaev, “Revised solution of ill-posed algebraic systems for noise data”, Comp. nanotechnol., 2015, 2,  14–19  mathnet  elib
4. M. M. Khapaev, T. M. Khapaeva, “On the Computation of Eigenfunctions and Eigenvalues in the Sturm–Liouville Problem”, Mat. Zametki, 97:4 (2015),  604–608  mathnet  mathscinet  zmath  elib; Math. Notes, 97:4 (2015), 616–620  isi  scopus
2009
5. V. V. Ternovskii, M. M. Khapaev, “Reconstruction of periodic functions from noisy input data”, Dokl. Akad. Nauk, 424:4 (2009),  452–454  mathnet  mathscinet; Dokl. Math., 79:1 (2009), 81–82  isi  scopus
2005
6. V. V. Ternovskii, A. M. Khapaev, M. M. Khapaev, “Resonance effects in the field of a stationary electromagnetic wave and a constant magnetic field”, TMF, 142:1 (2005),  64–71  mathnet  elib; Theoret. and Math. Phys., 142:1 (2005), 54–60  isi
2004
7. M. M. Khapaev, “Construction of the Solution of an Ill-Posed Singularly Perturbed Problem for the Heat Equation with a Nonlinearity”, Differ. Uravn., 40:6 (2004),  848–849  mathnet  mathscinet; Differ. Equ., 40:6 (2004), 908–910
2003
8. M. M. Khapaev, “Constructing Solutions of an Ill-Posed Nonlinear Singularly Perturbed Problem for an Equation of Elliptic Type”, Mat. Zametki, 73:2 (2003),  318–320  mathnet  mathscinet  zmath; Math. Notes, 73:2 (2003), 293–295  isi
2002
9. M. M. Khapaev, “On one ill-posed singularly perturbed problem”, Fundam. Prikl. Mat., 8:4 (2002),  1251–1254  mathnet  mathscinet  zmath
1999
10. M. M. Khapaev, A. A. Tsygankov, “An algorithm for solving the conditional extremum problem”, Differ. Uravn., 35:3 (1999),  310–312  mathnet  mathscinet; Differ. Equ., 35:3 (1999), 310–312
1995
11. M. M. Khapaev, “Differential equations that contain singular manifolds in control and minimization problems”, Differ. Uravn., 31:11 (1995),  1886–1892  mathnet  mathscinet; Differ. Equ., 31:11 (1995), 1854–1860
12. O. V. Anashkin, M. M. Khapaev, “On the partial stability of nonlinear systems of ordinary differential equations with a small parameter”, Differ. Uravn., 31:3 (1995),  371–381  mathnet  mathscinet; Differ. Equ., 31:3 (1995), 341–351
13. M. M. Khapaev, “Singular differential equations in control and minimization problems”, Trudy Mat. Inst. Steklov., 211 (1995),  411–418  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 211 (1995), 371–377
1993
14. M. M. Khapaev, “On taking into account measurement errors by the mathematical processing of them according to the Gauss least squares method”, Dokl. Akad. Nauk, 330:4 (1993),  444  mathnet  mathscinet  zmath; Dokl. Math., 47:3 (1993), 538–539
15. O. V. Anashkin, M. M. Khapaev, “On the stability of nonlinear systems with a small parameter”, Differ. Uravn., 29:8 (1993),  1301–1307  mathnet  mathscinet; Differ. Equ., 29:8 (1993), 1127–1132
1992
16. M. M. Khapaev, “Singular differential equations in control problems with constraints”, Dokl. Akad. Nauk, 324:6 (1992),  1166–1168  mathnet  mathscinet  zmath; Dokl. Math., 45:3 (1992), 706–709
17. M. M. Khapaev, “Singular differential equations in problems on the investigation of functions for a conditional extremum”, Dokl. Akad. Nauk, 323:2 (1992),  250–252  mathnet  mathscinet  zmath; Dokl. Math., 45:2 (1992), 322–324
18. O. V. Anashkin, M. M. Khapaev, “The method of Lyapunov functions for systems with perturbations”, Differ. Uravn., 28:12 (1992),  2027–2029  mathnet  mathscinet; Differ. Equ., 28:12 (1992), 1675–1677
1991
19. M. M. Khapaev, “Conditions for the controllability of singularly perturbed systems that contain singular controls”, Dokl. Akad. Nauk SSSR, 320:2 (1991),  300–302  mathnet  mathscinet  zmath; Dokl. Math., 44:2 (1992), 459–461
20. O. P. Filatov, M. M. Khapaev, “On the problem of the washing out of admixtures from a cavity”, Dokl. Akad. Nauk SSSR, 317:6 (1991),  1373–1375  mathnet  mathscinet; Dokl. Math., 36:4 (1991), 303–304
21. S. G. Osipov, M. M. Khapaev, “Modelling of micromagnetic structures”, Matem. Mod., 3:11 (1991),  12–38  mathnet  mathscinet  zmath
1990
22. M. M. Khapaev, “On the determination of averaged physical parameters in periodic media”, Dokl. Akad. Nauk SSSR, 315:4 (1990),  857–859  mathnet  mathscinet; Dokl. Math., 35:12 (1990), 1031–1032
23. M. M. Khapaev, “On the evolution of planetary orbits”, Dokl. Akad. Nauk SSSR, 312:3 (1990),  599–603  mathnet  mathscinet  zmath; Dokl. Math., 35:5 (1990), 431–433
24. S. G. Osipov, M. M. Khapaev, “On the nonlinear dynamics of a domain boundary”, Dokl. Akad. Nauk SSSR, 311:6 (1990),  1351–1355  mathnet  mathscinet; Dokl. Math., 35:4 (1990), 344–346
25. O. P. Filatov, M. M. Khapaev, “Averaging of differential inclusions with ‘fast’ and ‘slow’ variables”, Mat. Zametki, 47:6 (1990),  102–109  mathnet  mathscinet  zmath; Math. Notes, 47:6 (1990), 596–601  isi
26. O. P. Filatov, M. M. Khapaev, “Mutual $\varepsilon$-approximation of solutions of a system of differential inclusions and of the averaged”, Mat. Zametki, 47:5 (1990),  127–134  mathnet  mathscinet  zmath; Math. Notes, 47:5 (1990), 509–515  isi
1989
27. S. G. Osipov, V. V. Ternovskii, M. M. Khapaev, “Modelling of $3$-dimensional periodic structures in ferromagnetic films”, Dokl. Akad. Nauk SSSR, 305:4 (1989),  831–834  mathnet
28. O. V. Anashkin, M. M. Khapaev, “The comparison method and investigation of the stability of systems of ordinary differential equations containing perturbations. II”, Differ. Uravn., 25:2 (1989),  187–192  mathnet  mathscinet; Differ. Equ., 25:2 (1989), 133–137
1988
29. S. A. Trushin, M. M. Khapaev, G. V. Sholin, “Investigation of singularly perturbed equations that describe nonlinear magneto-acoustic waves”, Dokl. Akad. Nauk SSSR, 303:1 (1988),  74–77  mathnet  mathscinet; Dokl. Math., 33:11 (1988), 801–803
30. K. V. Mal'kov, M. M. Khapaev, “On the suppression of soliton-like solutions of shallow water equations by the outstripping resistance”, Dokl. Akad. Nauk SSSR, 300:5 (1988),  1052–1059  mathnet  mathscinet  zmath; Dokl. Math., 37:3 (1988), 777–783
31. S. G. Osipov, V. V. Ternovskii, M. M. Khapaev, “Properties of the solution of a nonlinear variational problem”, Differ. Uravn., 24:7 (1988),  1274–1276  mathnet  mathscinet  zmath
32. M. M. Khapaev, O. P. Filatov, “Stability of differential inclusions with multivalued perturbations”, Mat. Zametki, 43:3 (1988),  346–355  mathnet  mathscinet  zmath; Math. Notes, 43:3 (1988), 199–204  isi
1987
33. K. V. Mal'kov, M. M. Khapaev, “On the evolution and stability of soliton-like solutions of perturbed equations of Boussinesq type”, Dokl. Akad. Nauk SSSR, 292:1 (1987),  68–73  mathnet  mathscinet  zmath
34. K. V. Mal'kov, M. M. Khapaev, “Some methods in perturbation theory connected with averaging”, Differ. Uravn., 23:10 (1987),  1693–1704  mathnet  mathscinet  zmath
35. M. M. Khapaev, V. V. Balandin, “Construction of perturbations of Lyapunov functions and an investigation of stability under small random actions”, Differ. Uravn., 23:4 (1987),  675–680  mathnet  mathscinet
1986
36. M. M. Khapaev, K. V. Mal'kov, “Asymptotic behavior of solutions of differential equations with perturbations”, Dokl. Akad. Nauk SSSR, 290:4 (1986),  800–805  mathnet  mathscinet  zmath
37. M. M. Khapaev, G. V. Sholin, “Singularly perturbed systems containing singular manifolds”, Dokl. Akad. Nauk SSSR, 287:1 (1986),  99–103  mathnet  mathscinet
38. M. M. Khapaev, G. V. Sholin, “Analysis of plasma hydrodynamic equations by the methods of singularly perturbed systems”, Dokl. Akad. Nauk SSSR, 286:3 (1986),  602–605  mathnet
39. O. V. Anashkin, M. M. Khapaev, “The comparison method and investigation of the stability of systems of ordinary differential equations containing perturbations”, Differ. Uravn., 22:9 (1986),  1604–1606  mathnet  mathscinet  zmath
40. M. M. Khapaev, V. N. Shinkin, “Extremal properties of the Lyapunov function on unstable resonance regimes in the multifrequency case”, Differ. Uravn., 22:8 (1986),  1463–1466  mathnet  mathscinet  zmath
41. M. M. Khapaev, K. V. Mal'kov, “A class of methods for studying the asymptotic behavior of the solutions of differential equations with closed operators”, Differ. Uravn., 22:2 (1986),  255–267  mathnet  mathscinet
1985
42. I. V. Kuznetsova, M. M. Khapaev, “Investigation of the stability of systems containing perturbations”, Dokl. Akad. Nauk SSSR, 283:4 (1985),  810–813  mathnet  mathscinet  zmath
43. M. M. Khapaev, “A generalization of Lyapunov's second method and an investigation of the stability of applied problems”, Differ. Uravn., 21:10 (1985),  1730–1733  mathnet  mathscinet
1984
44. M. M. Khapaev, “An algorithm for the integration of singularly perturbed systems”, Dokl. Akad. Nauk SSSR, 278:6 (1984),  1313–1315  mathnet  mathscinet  zmath
1983
45. M. M. Khapaev, “A. N. Tikhonov's theorem for singularly perturbed systems”, Dokl. Akad. Nauk SSSR, 271:5 (1983),  1074–1077  mathnet  mathscinet  zmath
46. M. M. Khapaev, O. P. Filatov, “The averaging principle for systems with “fast” and “slow” variables”, Differ. Uravn., 19:9 (1983),  1640–1643  mathnet  mathscinet  zmath
1982
47. M. M. Khapaev, “On linear systems of ordinary differential equations”, Dokl. Akad. Nauk SSSR, 266:2 (1982),  299–301  mathnet  mathscinet  zmath
48. M. M. Khapaev, I. V. Kuznetsova, “Multifrequency systems that have lag”, Differ. Uravn., 18:2 (1982),  354–356  mathnet  mathscinet  zmath
1981
49. M. M. Khapaev, O. P. Filatov, “On averaging and stability in systems with singularities”, Dokl. Akad. Nauk SSSR, 261:1 (1981),  67–70  mathnet  mathscinet  zmath
50. M. M. Khapaev, O. P. Filatov, “Stability of resonance problems”, Differ. Uravn., 17:5 (1981),  949–953  mathnet  mathscinet  zmath
1980
51. M. M. Khapaev, A. I. Falin, “On the investigation of stability in systems of integrodifferential equations by the averaging method”, Dokl. Akad. Nauk SSSR, 250:2 (1980),  295–299  mathnet  mathscinet  zmath
52. M. M. Khapaev, “Problems of stability in systems of ordinary differential equations”, Uspekhi Mat. Nauk, 35:1(211) (1980),  127–170  mathnet  mathscinet  zmath; Russian Math. Surveys, 35:1 (1980), 145–197  isi
1979
53. M. M. Khapaev, O. V. Anashkin, “Stability in systems of ordinary differential equations with almost periodic coefficients”, Differ. Uravn., 15:7 (1979),  1216–1224  mathnet  mathscinet  zmath
1978
54. M. M. Khapaev, O. V. Anashkin, “On the investigation of stability in systems of ordinary differential equations with almost-periodic coefficients”, Dokl. Akad. Nauk SSSR, 240:5 (1978),  1028–1031  mathnet  mathscinet  zmath
1976
55. M. M. Khapaev, “A study of stability in the three body problem on the basis of a hydrodynamical model of the planets”, Dokl. Akad. Nauk SSSR, 231:5 (1976),  1092–1095  mathnet  mathscinet
1974
56. M. M. Khapaev, “On averaging in multifrequency systems”, Dokl. Akad. Nauk SSSR, 217:5 (1974),  1021–1024  mathnet  mathscinet  zmath
57. M. M. Khapaev, “A stability analysis of resonance problems”, Differ. Uravn., 10:3 (1974),  447–457  mathnet  mathscinet  zmath
1973
58. M. M. Khapaev, “A generalization of Ljapunov's second method”, Differ. Uravn., 9:11 (1973),  2020–2028  mathnet  mathscinet  zmath
1970
59. M. M. Khapaev, “Stability in the problem of three bodies”, Dokl. Akad. Nauk SSSR, 195:2 (1970),  300–302  mathnet  mathscinet  zmath
60. M. M. Khapaev, “Generalization of Ljapunov’s second method and the investigation of some resonance problems”, Dokl. Akad. Nauk SSSR, 193:1 (1970),  46–49  mathnet  mathscinet  zmath
1969
61. M. M. Khapaev, “The stability of the state of equilibrium of systems of differential equations”, Differ. Uravn., 5:5 (1969),  848–855  mathnet  mathscinet  zmath
1968
62. M. M. Khapaev, “Instability under constantly acting perturbations”, Dokl. Akad. Nauk SSSR, 178:1 (1968),  47–50  mathnet  mathscinet  zmath
63. M. M. Khapaev, “Investigation of stability in the theory of nonlinear oscillations”, Mat. Zametki, 3:3 (1968),  307–318  mathnet  mathscinet  zmath; Math. Notes, 3:3 (1968), 194–200
1967
64. M. M. Khapaev, “A theorem of Ljapunov type”, Dokl. Akad. Nauk SSSR, 176:6 (1967),  1262–1265  mathnet  mathscinet  zmath
1966
65. M. M. Khapaev, “On the averaging method in certain problems connected with averaging”, Differ. Uravn., 2:5 (1966),  600–608  mathnet  mathscinet
66. M. M. Khapaev, “Жесткая фокусировка гофрированным магнитным полем”, Zh. Vychisl. Mat. Mat. Fiz., 6:supplement to № 4 (1966),  75–79  mathnet
1965
67. M. M. Khapaev, “Non linear theory of the motion of fast charged particles in helical toroidal magnetic fields”, Dokl. Akad. Nauk SSSR, 163:2 (1965),  343–346  mathnet
1962
68. M. M. Khapaev, “Asymptotic behavior in the neighborhood of an irregular singular point of the solutions of ordinary differential equations with small coefficients on the highest derivatives”, Mat. Sb. (N.S.), 57(99):2 (1962),  187–200  mathnet  mathscinet  zmath
1961
69. M. M. Khapaev, “Asymptotic expansions of hypergeometric and confluent hypergeometric functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1961, 5,  98–101  mathnet  mathscinet  zmath
70. M. M. Khapaev, “Linear differential equations with small coefficients of several higher derivatives in the neighborhood of regular singular points of the equation”, Uspekhi Mat. Nauk, 16:4(100) (1961),  187–194  mathnet  mathscinet  zmath
1960
71. M. M. Khapaev, “Asymptotic expansions of the solutions of ordinary linear differential equations in the neighborhood of an irregular singularity when the coefficients of the higher derivatives in the equations are small”, Dokl. Akad. Nauk SSSR, 135:6 (1960),  1338–1341  mathnet  mathscinet  zmath

1986
72. I. V. Kuznetsova, M. M. Khapaev, “Correction: “Investigation of the stability of systems containing perturbations””, Dokl. Akad. Nauk SSSR, 288:6 (1986),  1288  mathnet  mathscinet

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