RUS  ENG
Full version
PEOPLE

Galaktionov Viktor Aleksandrovich

Publications in Math-Net.Ru

  1. Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical Fujita range: second-order diffusion

    Adv. Nonlinear Stud., 14:1 (2014),  1–29
  2. The KPP-problem and $\log t$-front shift for higher-order semilinear parabolic equations

    Trudy Mat. Inst. Steklova, 283 (2013),  49–79
  3. Global sign-changing solutions of a higher order semilinear heat equation in the subcritical Fujita range

    Adv. Nonlinear Stud., 12:3 (2012),  569–596
  4. On Nonexistence of Baras–Goldstein Type without Positivity Assumptions for Singular Linear and Nonlinear Parabolic Equations

    Trudy Mat. Inst. Steklova, 260 (2008),  130–150
  5. Nonlinear dispersion equations: Smooth deformations, compactions, and extensions to higher orders

    Zh. Vychisl. Mat. Mat. Fiz., 48:10 (2008),  1859
  6. Third-order nonlinear dispersive equations: Shocks, rarefaction, and blowup waves

    Zh. Vychisl. Mat. Mat. Fiz., 48:10 (2008),  1819–1846
  7. Convergence in gradient systems with branching of equilibria

    Mat. Sb., 198:6 (2007),  65–88
  8. On the absence of global solutions of nonlinear mixed problems

    Tr. Semim. im. I. G. Petrovskogo, 26 (2007),  73–91
  9. Conditions for the existence of solutions to a quasilinear inequality in half-space

    Mat. Zametki, 67:1 (2000),  150–152
  10. Ordered invariant sets for KdV-type nonlinear evolution equations

    Zh. Vychisl. Mat. Mat. Fiz., 39:9 (1999),  1564–1570
  11. Maximal Sign-Invariants and New Exact Solutions of Quasilinear Parabolic Equations with Gradient Diffusivity

    Keldysh Institute preprints, 1997, 098
  12. Generalized separation of variables for differential equations with polynomial nonlinearities

    Differ. Uravn., 31:2 (1995),  253–261
  13. Exact solutions and invariant spaces for nonlinear gradient diffusion equations

    Zh. Vychisl. Mat. Mat. Fiz., 34:3 (1994),  373–383
  14. On a general approach to extinction and blow-up for quasi-linear heat equations

    Zh. Vychisl. Mat. Mat. Fiz., 33:2 (1993),  246–258
  15. The space structure near a blow-up point for semilinear heat equations: A formal approach

    Zh. Vychisl. Mat. Mat. Fiz., 31:3 (1991),  399–411
  16. Asymptotic behavior of solutions of a nonlinear diffusion-absorption equation with a critical exponent

    Dokl. Akad. Nauk SSSR, 314:3 (1990),  530–534
  17. The monotonicity property for a quasilinear degenerate parabolic equation

    Differ. Uravn., 26:7 (1990),  1127–1136
  18. Estimates from below for unbounded solutions of a quasilinear parabolic system of equations

    Mat. Zametki, 47:2 (1990),  8–14
  19. Accurate estimates for the amplitude and support of unbounded solutions of the nonlinear heat-conduction equation with a source

    Zh. Vychisl. Mat. Mat. Fiz., 30:3 (1990),  438–448
  20. A sharp estimate for the support of the unbounded solution of a quasilinear degenerate parabolic equation

    Dokl. Akad. Nauk SSSR, 309:2 (1989),  265–268
  21. Modelling of sharpening processes in heat transfer problems with nonlinear source

    Mat. Model., 1:12 (1989),  89–108
  22. A proof of localization of unbounded solutions for quasilinear heat equation with a source

    Mat. Model., 1:3 (1989),  75–83
  23. On the method of stationary states for quasilinear parabolic equations

    Mat. Sb., 180:8 (1989),  995–1016
  24. New exact solutions of parabolic equations with quadratic nonlinearities

    Zh. Vychisl. Mat. Mat. Fiz., 29:4 (1989),  497–506
  25. Localization in a nonlinear problem of radiation-induced ignition

    Dokl. Akad. Nauk SSSR, 302:1 (1988),  68–71
  26. The structure of limit distributions of unbounded solutions of quasilinear parabolic equations

    Dokl. Akad. Nauk SSSR, 301:4 (1988),  781–785
  27. A method of investigating unbounded solutions of quasilinear parabolic equations

    Zh. Vychisl. Mat. Mat. Fiz., 28:6 (1988),  842–854
  28. A nonlinear boundary value problem of ignition by radiation

    Zh. Vychisl. Mat. Mat. Fiz., 28:4 (1988),  549–559
  29. Estimates for localized unbounded solutions of quasilinear parabolic equations

    Differ. Uravn., 23:7 (1987),  1133–1143
  30. Asymptotic behavior of unbounded solutions of the nonlinear equation $u_t=(u^\sigma u_x)_x+u^\beta$ near a “singular” point

    Dokl. Akad. Nauk SSSR, 288:6 (1986),  1293–1297
  31. A nonlinear equation of “rapid diffusion” in $\mathbf{R}^N$

    Dokl. Akad. Nauk SSSR, 287:3 (1986),  539–542
  32. Application of new comparison theorems to the investigation of unbounded solutions of nonlinear parabolic equations

    Differ. Uravn., 22:7 (1986),  1165–1173
  33. A quasilinear equation of heat conduction with a source: peaking, localization, symmetry, exact solutions, asymptotic behavior, structures

    Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 28 (1986),  95–205
  34. A nonlinear elliptic problem with a complex spectrum of solutions

    Zh. Vychisl. Mat. Mat. Fiz., 26:3 (1986),  398–407
  35. Asymptotic stability of self-similar solutions of an equation of heat conduction with a nonlinear sink

    Dokl. Akad. Nauk SSSR, 281:1 (1985),  23–28
  36. A nonlinear problem of laser thermochemistry. II

    Differ. Uravn., 21:12 (1985),  2097–2105
  37. A nonlinear problem of laser thermochemistry. I

    Differ. Uravn., 21:11 (1985),  1947–1958
  38. A parabolic system of quasilinear equations. II

    Differ. Uravn., 21:9 (1985),  1544–1559
  39. Asymptotic behavior of unbounded solutions of the nonlinear parabolic equation $u_t=(u^\sigma u_x)_x+u^{\sigma+1}$

    Differ. Uravn., 21:7 (1985),  1126–1134
  40. A proof of the localization of unbounded solutions of the nonlinear parabolic equation $u_t=(u^\sigma u_x)_x+u^\beta$

    Differ. Uravn., 21:1 (1985),  15–23
  41. On asymptotic “eigenfunctions” of the Cauchy problem for a nonlinear parabolic equation

    Mat. Sb. (N.S.), 126(168):4 (1985),  435–472
  42. A new class of asymptotic “eigenfunctions” of the Cauchy problem for a nonlinear parabolic equation

    Zh. Vychisl. Mat. Mat. Fiz., 25:12 (1985),  1833–1839
  43. A nonlinear problem of laser thermochemistry

    Dokl. Akad. Nauk SSSR, 279:4 (1984),  838–842
  44. On the method of stationary states for nonlinear evolution parabolic problems

    Dokl. Akad. Nauk SSSR, 278:6 (1984),  1296–1300
  45. An equation of nonlinear heat conduction with nonpower coefficient in a bounded domain

    Dokl. Akad. Nauk SSSR, 275:2 (1984),  285–289
  46. Asymptotic stability of invariant solutions of nonlinear equations of heat conduction with a source

    Differ. Uravn., 20:4 (1984),  614–632
  47. On approximate self-similar solutions of a class of quasilinear heat equations with a source

    Mat. Sb. (N.S.), 124(166):2(6) (1984),  163–188
  48. A parabolic system of quasilinear equations. I

    Differ. Uravn., 19:12 (1983),  2123–2140
  49. Methods of constructing approximate self-similar solutions of nonlinear heat equations. IV

    Mat. Sb. (N.S.), 121(163):2(6) (1983),  131–155
  50. Methods of constructing approximate self-similar solutions of nonlinear heat equations. III

    Mat. Sb. (N.S.), 120(162):1 (1983),  3–21
  51. Conditions for global non-existence and localizations of solutions of the Cauchy problem for a class of non-linear parabolic equations

    Zh. Vychisl. Mat. Mat. Fiz., 23:6 (1983),  1341–1354
  52. On the global unsolvability of Cauchy problems for quasilinear parabolic equations

    Zh. Vychisl. Mat. Mat. Fiz., 23:5 (1983),  1072–1087
  53. Difference solutions of a class of quasilinear parabolic equations. II

    Zh. Vychisl. Mat. Mat. Fiz., 23:4 (1983),  831–838
  54. Difference solutions of a class of quasilinear parabolic equations. I

    Zh. Vychisl. Mat. Mat. Fiz., 23:3 (1983),  646–659
  55. Critical conditions and comparison theorems for difference solutions of nonlinear parabolic equations

    Zh. Vychisl. Mat. Mat. Fiz., 23:1 (1983),  109–118
  56. Approximate self-similar solutions of the heat equation

    Dokl. Akad. Nauk SSSR, 265:4 (1982),  784–789
  57. On localization conditions for unbounded solutions of quasilinear parabolic equations

    Dokl. Akad. Nauk SSSR, 264:5 (1982),  1035–1040
  58. Methods of constructing approximate self-similar solutions of nonlinear heat equations. II

    Mat. Sb. (N.S.), 118(160):4(8) (1982),  435–455
  59. Methods of constructing approximate self-similar solutions of nonlinear heat equations. I

    Mat. Sb. (N.S.), 118(160):3(7) (1982),  291–322
  60. The existence and non-existence of global solutions of boundary value problems for quasi-linear parabolic equations

    Zh. Vychisl. Mat. Mat. Fiz., 22:6 (1982),  1369–1385
  61. Conditions for the absence of global solutions of a class of quasilinear parabolic equations

    Zh. Vychisl. Mat. Mat. Fiz., 22:2 (1982),  322–338
  62. Localization of heat in nonlinear media

    Differ. Uravn., 17:10 (1981),  1826–1841
  63. A boundary value problem for the nonlinear parabolic equation $u_t=\Delta u^{\sigma+1}+u^\beta$

    Differ. Uravn., 17:5 (1981),  836–842
  64. Some properties of travelling waves in a medium with nonlinear thermal conductivity and a source of heat

    Zh. Vychisl. Mat. Mat. Fiz., 21:4 (1981),  980–989
  65. Unbounded solutions of the Cauchy problem for the parabolic equation $u_t=\nabla(u^\sigma\nabla u)+u^\beta$

    Dokl. Akad. Nauk SSSR, 252:6 (1980),  1362–1364
  66. Approximate self-similar solutions of equations of heat conduction type

    Differ. Uravn., 16:9 (1980),  1660–1676
  67. Asymptotic phase of modes with peaking and effective localization of heat in problems of nonlinear heat conduction

    Differ. Uravn., 16:7 (1980),  1196–1204
  68. Comparison of solutions to parabolic equations

    Dokl. Akad. Nauk SSSR, 248:3 (1979),  586–589
  69. Localization of diffusion processes in media with constant properties

    Dokl. Akad. Nauk SSSR, 247:2 (1979),  349–353
  70. An approach to the comparison of solutions of parabolic equations

    Zh. Vychisl. Mat. Mat. Fiz., 19:6 (1979),  1451–1461

  71. Letter to the editor: “Estimates for localized unbounded solutions of quasilinear parabolic equations”

    Differ. Uravn., 24:3 (1988),  545
  72. Letter to the Editor

    Mat. Sb. (N.S.), 131(173):3(11) (1986),  413
  73. Letter to the Editor

    Mat. Sb. (N.S.), 121(163):2(6) (1983),  286

© Steklov Math. Inst. of RAS, 2026