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Butuzov Valentin Fedorovich

Publications in Math-Net.Ru

  1. Singularly perturbed partially dissipative systems of equations

    TMF, 207:2 (2021),  210–225
  2. Asymptotics of a steplike contrast structure in a partially dissipative stationary system of equations

    Zh. Vychisl. Mat. Mat. Fiz., 61:1 (2021),  57–84
  3. On singularly perturbed systems of ODE with a multiple root of the degenerate equation

    Izv. RAN. Ser. Mat., 84:2 (2020),  60–89
  4. Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation

    Mat. Sb., 210:11 (2019),  76–102
  5. Asymptotic expansion of the solution to a partially dissipative system of equations with a multizone boundary layer

    Zh. Vychisl. Mat. Mat. Fiz., 59:10 (2019),  1731–1751
  6. Asymptotic behavior and stability of a stationary boundary-layer solution to a partially dissipative system of equations

    Zh. Vychisl. Mat. Mat. Fiz., 59:7 (2019),  1201–1229
  7. Existence, asymptotics, stability and region of attraction of a periodic boundary layer solution in case of a double root of the degenerate equation

    Zh. Vychisl. Mat. Mat. Fiz., 58:12 (2018),  1989–2001
  8. On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer

    Zh. Vychisl. Mat. Mat. Fiz., 58:6 (2018),  961–987
  9. Asymptotic behaviour and stability of solutions of a singularly perturbed elliptic problem with a triple root of the degenerate equation

    Izv. RAN. Ser. Mat., 81:3 (2017),  21–44
  10. On contrast structures with a multizonal interior layer

    Model. Anal. Inform. Sist., 24:3 (2017),  288–308
  11. Singularly perturbed elliptic Dirichlet problem with a multiple root of the degenerate equation

    Model. Anal. Inform. Sist., 23:5 (2016),  515–528
  12. Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation

    Model. Anal. Inform. Sist., 23:3 (2016),  248–258
  13. On the Dependence of the Structure of Boundary Layers on the Boundary Conditions in a Singularly Perturbed Boundary-Value Problem with Multiple Root of the Related Degenerate Equation

    Mat. Zametki, 99:2 (2016),  201–214
  14. Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation

    Mat. Sb., 207:8 (2016),  73–100
  15. Asymptotics of the solution to a singularly perturbed elliptic problem with a three-zone boundary layer

    Zh. Vychisl. Mat. Mat. Fiz., 56:8 (2016),  1428–1440
  16. Asymptotics of the solution to an initial boundary value problem for a singularly perturbed parabolic equation in the case of a triple root of the degenerate equation

    Zh. Vychisl. Mat. Mat. Fiz., 56:4 (2016),  605–624
  17. The initial-boundary value problem for a singularly perturbed parabolic equation in the case of double and triple root of the degenerate equation

    Chebyshevskii Sb., 16:4 (2015),  41–76
  18. Singularly perturbed boundary value problem with multizonal interior transitional layer

    Model. Anal. Inform. Sist., 22:1 (2015),  5–22
  19. Corner Boundary Layer in Nonlinear Elliptic Problems Containing Derivatives of First Order

    Model. Anal. Inform. Sist., 21:1 (2014),  7–31
  20. On the Special Properties of the Boundary Layer in Singularly Perturbed Problems with Multiple Root of the Degenerate Equation

    Mat. Zametki, 94:1 (2013),  68–80
  21. A steplike contrast structure in a singularly perturbed system of elliptic equations

    Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013),  1427–1447
  22. A singularly perturbed elliptic problem in the case of a multiple root of the degenerate equation

    Zh. Vychisl. Mat. Mat. Fiz., 53:8 (2013),  1291–1301
  23. Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter

    Zh. Vychisl. Mat. Mat. Fiz., 52:11 (2012),  1983–2003
  24. Singularly perturbed partially dissipative reaction-diffusion systems in the case of intersecting roots of the degenerate equation

    Chebyshevskii Sb., 12:3 (2011),  22–44
  25. On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation

    Zh. Vychisl. Mat. Mat. Fiz., 51:1 (2011),  44–55
  26. Singularly perturbed problems with boundary and internal layers

    Trudy Mat. Inst. Steklova, 268 (2010),  268–283
  27. Singularly perturbed two-dimensional parabolic problem in the case of intersecting roots of the reduced equation

    Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007),  646–654
  28. On a singularly perturbed system of first-order partial differential equations with various degrees of a small parameter

    Differ. Uravn., 42:6 (2006),  775–789
  29. Existence and asymptotic stability of a stationary solution of a singularly perturbed system of parabolic equations in the case of intersecting roots of the degenerate equation

    Differ. Uravn., 42:2 (2006),  221–232
  30. On the stability and domain of attraction of a stationary nonsmooth limit solution of a singularly perturbed parabolic equation

    Zh. Vychisl. Mat. Mat. Fiz., 46:3 (2006),  433–444
  31. Singular Perturbation Elliptic Boundary-Value Problems in the Case of a Nonisolated Root of the Degenerate Equation

    Mat. Zametki, 78:1 (2005),  26–36
  32. On the Formation of a Solution with an Internal Layer in a Parabolic System with Different Powers of a Small Parameter

    Differ. Uravn., 40:3 (2004),  356–367
  33. Global domain of attraction of a step-like contrast structure in a critical case

    Zh. Vychisl. Mat. Mat. Fiz., 44:8 (2004),  1410–1431
  34. On the global domain of influence of stable steplike contrast structures in the Dirichlet problem

    Zh. Vychisl. Mat. Mat. Fiz., 44:6 (2004),  1039–1061
  35. Singularly perturbed parabolic problem in the case of intersecting roots of the degenerate equation

    Trudy Inst. Mat. i Mekh. UrO RAN, 9:1 (2003),  38–44
  36. Asymptotic behavior of the solution of a singularly perturbed system of reaction-diffusion equations in a thin rod

    Zh. Vychisl. Mat. Mat. Fiz., 43:8 (2003),  1160–1182
  37. On a system of reaction-diffusion-transfer type in the case of small diffusion and fast reactions

    Zh. Vychisl. Mat. Mat. Fiz., 43:7 (2003),  1005–1017
  38. Instability of Multidimensional Contrast Structures

    Differ. Uravn., 38:2 (2002),  222–233
  39. The Stability of a Step-Like Contrast Structure in the Case of a Multiple Root of the Equation for the Transition Point

    Differ. Uravn., 38:1 (2002),  70–80
  40. On the global domain of influence of stable solutions with interior layers in the two-dimensional case

    Izv. RAN. Ser. Mat., 66:1 (2002),  3–42
  41. System of singularly perturbed equations in the case of intersecting roots of a degenerate system

    Zh. Vychisl. Mat. Mat. Fiz., 42:11 (2002),  1686–1699
  42. On a singularly perturbed system of parabolic equations in the case of intersecting roots of the degenerate equation

    Zh. Vychisl. Mat. Mat. Fiz., 42:2 (2002),  185–196
  43. A Two-Dimensional Step-Like Contrast Structure in the Case of a Multiple Root of the Transition Line Equation

    Differ. Uravn., 37:4 (2001),  495–510
  44. A Step-Like Contrast Structure for the Case of a Multiple Root of the Transition Point Equation (the Critical Case)

    Differ. Uravn., 37:2 (2001),  171–180
  45. Step-type contrast structure in a system of two singularly perturbed parabolic equations

    Matem. Mod., 13:12 (2001),  23–42
  46. Global influence domains of stable solutions with internal layers

    Mat. Sb., 192:5 (2001),  13–52
  47. Boundary value problem for a system of fast and slow second-order equations in the case of intersecting roots of the degenerate equation

    Zh. Vychisl. Mat. Mat. Fiz., 41:8 (2001),  1165–1179
  48. Asymptotic stability of solutions of singularly perturbed boundary value problems with boundary and internal layers

    Differ. Uravn., 36:2 (2000),  198–208
  49. Asymptotics of the solution of a system of equations in partial derivatives of the first order with a small parameter at some derivatives

    Fundam. Prikl. Mat., 6:3 (2000),  723–738
  50. A steplike contrast structure in a singularly perturbed system of elliptic equations with different power of a small parameter

    Zh. Vychisl. Mat. Mat. Fiz., 40:6 (2000),  877–899
  51. A limit theorem for a Tikhonov system of equations

    Zh. Vychisl. Mat. Mat. Fiz., 40:5 (2000),  703–713
  52. On periodic contrast structures in singularly perturbed elliptic equations

    Fundam. Prikl. Mat., 5:2 (1999),  385–409
  53. Existence, local uniqueness, and asymptotics of two-dimensional periodic steplike contrast structures

    Zh. Vychisl. Mat. Mat. Fiz., 39:5 (1999),  812–831
  54. A step-type contrast structure in the case of a multiple root of the equation for a transition point

    Differ. Uravn., 34:8 (1998),  1029–1038
  55. A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability

    Mat. Zametki, 63:3 (1998),  354–362
  56. Asymptotic Theory of Contrasting Structures. A Survey

    Avtomat. i Telemekh., 1997, no. 7,  4–32
  57. Spikelike contrast structures in the parabolic system of two singularly perturbed equations

    Zh. Vychisl. Mat. Mat. Fiz., 37:4 (1997),  415–428
  58. Space-periodic contrast structures in singularly perturbed elliptic problems

    Dokl. Akad. Nauk, 351:6 (1996),  731–734
  59. Asymptotic behavior of the solution of the heat equation with a nonlinear heat source in a thin rod

    Zh. Vychisl. Mat. Mat. Fiz., 36:6 (1996),  68–85
  60. Asymptotic expansion of the solution of a boundary value problem for the heat equation with a powerful nonlinear source in a thin rod

    Differ. Uravn., 31:3 (1995),  472–482
  61. On a singularly perturbed reaction-diffusion-transfer system in the case of slow diffusion and fast reactions

    Fundam. Prikl. Mat., 1:4 (1995),  907–922
  62. One singularly perturbed system of partial differential equations of the first order

    Mat. Zametki, 57:3 (1995),  338–349
  63. A singularly perturbed “reaction–diffusion–transfer” system which degenerates into a system with a finite equation and a first-order partial differential equation

    Zh. Vychisl. Mat. Mat. Fiz., 35:2 (1995),  223–240
  64. Asymptotics of the solution of non-stationary interface convection problem in thin layer of viscous liquid

    Matem. Mod., 6:5 (1994),  92–104
  65. A singulary perturbed “reaction–diffusion–transfer” system which degenerates into a system of two first-order differential equations

    Zh. Vychisl. Mat. Mat. Fiz., 34:10 (1994),  1380–1400
  66. Singularly perturbed systems of reaction-diffusion-transport type

    Differ. Uravn., 29:5 (1993),  833–845
  67. Asymptotical deduction of the ambipolar diffusion equation and boundary conditions in semiconductor physics

    Matem. Mod., 4:8 (1992),  66–74
  68. The asymptotic behaviour of the solution of a singularly perturbed two-dimensional problem of the reaction-diffusion-transport type

    Zh. Vychisl. Mat. Mat. Fiz., 31:4 (1991),  533–542
  69. A singularly perturbed system of equations of elliptic type

    Differ. Uravn., 26:2 (1990),  271–278
  70. Asymptotic solution of Marangony convection problem in a thin layer of viscous liquid

    Matem. Mod., 2:8 (1990),  76–89
  71. Asymptotic approximation of the solution of a singularly perturbed parabolic two-dimensional problem with a nonsmooth limit solution

    Differ. Uravn., 25:12 (1989),  2128–2133
  72. On the asymptotic behavior of the solution of a singularly perturbed parabolic problem in the two-dimensional case

    Differ. Uravn., 25:3 (1989),  453–461
  73. The asymptotic solution of linearized problems on the natural and forced resonance oscillations of a medium of low viscosity

    Zh. Vychisl. Mat. Mat. Fiz., 29:7 (1989),  1023–1035
  74. An angular boundary layer in the asymptotics of the solution of a singularly perturbed system of equations of elliptic type

    Differ. Uravn., 24:2 (1988),  343–345
  75. Asymptotic behaviour of the solution of the problem of combustion in the case of an autocatalytic reaction

    Zh. Vychisl. Mat. Mat. Fiz., 28:5 (1988),  683–694
  76. The asymptotic theory of contrasting spatial structures

    Zh. Vychisl. Mat. Mat. Fiz., 28:3 (1988),  346–361
  77. Asymptotic of a solution of contrast-structure type

    Mat. Zametki, 42:6 (1987),  831–841
  78. On a singularly perturbed quasilinear parabolic problem with unsmooth corner boundary functions

    Zh. Vychisl. Mat. Mat. Fiz., 27:7 (1987),  1012–1021
  79. A smoothing procedure in a singularly perturbed quasilinear parabolic problem

    Zh. Vychisl. Mat. Mat. Fiz., 27:3 (1987),  391–399
  80. Asymptotic solution of the linearized problem of the propagation of sound in a bounded medium with low viscosity

    Zh. Vychisl. Mat. Mat. Fiz., 27:2 (1987),  226–236
  81. Some singularly perturbed problems of hyperbolic type with transition layers

    Differ. Uravn., 22:10 (1986),  1739–1744
  82. A singularly perturbed system of equations of elliptic type in the critical case

    Differ. Uravn., 22:9 (1986),  1565–1576
  83. Asymptotic approximation of solution of boundary-value problem for singularly disturbed parabolic equation in the critical case

    Mat. Zametki, 39:6 (1986),  819–830
  84. A singularly perturbed boundary value problem of elliptic type with nonsmooth angular boundary layer functions

    Differ. Uravn., 21:10 (1985),  1751–1755
  85. The method of boundary layer functions

    Differ. Uravn., 21:10 (1985),  1662–1669
  86. Singularly disturbed elliptic boundary value problem in a rectangle in the critical case

    Zh. Vychisl. Mat. Mat. Fiz., 24:9 (1984),  1320–1330
  87. On some singularly perturbed problems with nonsmooth boundary functions

    Dokl. Akad. Nauk SSSR, 263:4 (1982),  786–789
  88. A singularly perturbed boundary value problem of elliptic type in the critical case

    Differ. Uravn., 18:6 (1982),  1056–1061
  89. The asymptotics of the solution of an equation of parabolic type with small parameters multiplying the highest derivatives

    Zh. Vychisl. Mat. Mat. Fiz., 22:4 (1982),  865–870
  90. On a system of singularly perturbed equations of elliptic type

    Differ. Uravn., 17:10 (1981),  1779–1791
  91. Asymptotic solution of a system of singularly perturbed equations of elliptic type with angular boundary layer

    Zh. Vychisl. Mat. Mat. Fiz., 21:3 (1981),  665–677
  92. An angular boundary layer in singularly perturbed problems with partial derivatives

    Differ. Uravn., 15:10 (1979),  1848–1862
  93. The asymptotics of solutions of some model problems in chemical kinetics, taking diffusion into account

    Dokl. Akad. Nauk SSSR, 242:2 (1978),  268–271
  94. Angular boundary layer in singularly perturbed mixed problems for the second-order hyperbolic equations

    Dokl. Akad. Nauk SSSR, 235:5 (1977),  997–1000
  95. The construction of boundary functions in certain singularly perturbed problems of elliptic type

    Differ. Uravn., 13:10 (1977),  1829–1835
  96. The angular boundary layer in mixed singularly perturbed problems for hyperbolic equations

    Mat. Sb. (N.S.), 104(146):3(11) (1977),  460–485
  97. A singularly perturbed equation of elliptic type with two small parameters

    Differ. Uravn., 12:10 (1976),  1793–1803
  98. A problem in the theory of singular perturbations

    Differ. Uravn., 12:10 (1976),  1736–1747
  99. The asymptotic behavior of the solutions of singularly perturbed equations of elliptic type in a rectangular domain

    Differ. Uravn., 11:6 (1975),  1030–1041
  100. Asymptotic behavior of the solution of the equation $\mu^2\Delta u-k^2(x,y)u=f(x,y)$ in a rectangular domain

    Differ. Uravn., 9:9 (1973),  1654–1660
  101. Asymptotic properties of the solution of a finite-difference equation with small steps in a rectangular region

    Zh. Vychisl. Mat. Mat. Fiz., 12:3 (1972),  582–597
  102. A certain integro-differential equation with a small parameter multiplying the derivative in the case when the degenerate equation occurs in the spectrum

    Differ. Uravn., 7:5 (1971),  919–922
  103. Differential and difference systems of equations with a small parameter in the case when the unperturbed (degenerate) system is situated on the spectrum

    Differ. Uravn., 6:4 (1970),  650–664
  104. Asymptotic methods in the theory of ordinary differential equations

    Itogi Nauki. Ser. Matematika. Mat. Anal. 1967, 1969,  5–73
  105. Asymptotics of the solution of a certain problem for a nonlinear integro-differential equation with a small parameter at the derivative

    Differ. Uravn., 4:3 (1968),  491–507
  106. On the question of the asymptotics of solutions to integro-differential equations with a small parameter in front of the derivative

    Differ. Uravn., 2:3 (1966),  391–406
  107. Certain problems on eigenvalues for integro-differential equations with a small parameter coefficient for the higher derivative

    Differ. Uravn., 1:9 (1965),  1190–1203
  108. Asymptotic behaviour of the solution of an integro-differential equation with a small parameter multiplying the derivative

    Zh. Vychisl. Mat. Mat. Fiz., 4:supplement to № 4 (1964),  183–191

  109. К семидесятипятилетию Александра Николаевича Боголюбова

    Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020),  1451–1452
  110. Vasilii Vasilievich Zhikov

    Tr. Semim. im. I. G. Petrovskogo, 32 (2019),  5–7
  111. From the editors of the special issue

    Model. Anal. Inform. Sist., 24:3 (2017),  257
  112. On the 70th anniversary of birthday of Professor Aleksandr Nikolaevich Bogolyubov

    Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015),  1635–1636
  113. Aleksei Georgievich Sveshnikov (on his 80th birthday)

    Uspekhi Mat. Nauk, 60:2(362) (2005),  187–190
  114. Aleksei Georgievich Sveshnikov (on the occasion of his eightieth birthday)

    Zh. Vychisl. Mat. Mat. Fiz., 45:3 (2005),  371–373
  115. Contrast structures in singularly perturbed problems

    Fundam. Prikl. Mat., 4:3 (1998),  799–851
  116. Конференция “Теория и приложения методов малого параметра”, посвященная 90-летию со дня рождения академика А. Н. Тихонова (Обнинск, 2–6 июля 1998 г.)

    Differ. Uravn., 32:10 (1996),  1436
  117. Adelaida Borisovna Vasil'eva (on her seventieth birthday)

    Uspekhi Mat. Nauk, 51:4(310) (1996),  177–178
  118. Aleksei Georgievich Sveshnikov (on his seventieth birthday)

    Uspekhi Mat. Nauk, 50:1(301) (1995),  219–220
  119. Mikhail Mikhaǐlovich Khapaev (on the occasion of his sixtieth birthday)

    Differ. Uravn., 30:10 (1994),  1830–1835
  120. Èduard Genrikhovich Poznyak (on the occasion of his seventieth birthday)

    Differ. Uravn., 29:12 (1993),  2032–2033
  121. Eduard Genrikhovich Poznyak (on his seventieth birthday)

    Uspekhi Mat. Nauk, 48:4(292) (1993),  245–247
  122. Adelaida Borisovna Vasil'eva (on her sixtieth birthday)

    Uspekhi Mat. Nauk, 41:5(251) (1986),  205–206
  123. The Second All-Union conference on asymptotic methods in the theory of singularly perturbed equations

    Uspekhi Mat. Nauk, 35:1(211) (1980),  240–241

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