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Shishmarev Il'ya Andreevich

Publications in Math-Net.Ru

  1. Asymptotic expansion of solutions to the periodic problem for a non-linear Sobolev-type equation

    Izv. RAN. Ser. Mat., 77:2 (2013),  97–108
  2. The far-field asymptotics of solutions of a fractional non-linear equation

    Izv. RAN. Ser. Mat., 76:2 (2012),  37–66
  3. Periodic Boundary Value Problem for Nonlinear Sobolev-Type Equations

    Funktsional. Anal. i Prilozhen., 44:3 (2010),  14–26
  4. A boundary-value problem for a non-linear equation with a fractional derivative

    Izv. RAN. Ser. Mat., 73:6 (2009),  101–124
  5. Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

    Uspekhi Mat. Nauk, 64:3(387) (2009),  3–72
  6. On a nonlinear Sobolev type equation

    Differ. Uravn., 41:1 (2005),  138–140
  7. The Cauchy problem for an equation of Sobolev type with power non-linearity

    Izv. RAN. Ser. Mat., 69:1 (2005),  61–114
  8. Asymptotics of solutions of non-linear dissipative equations

    Izv. RAN. Ser. Mat., 68:3 (2004),  29–62
  9. Cauchy problem for non-linear systems of equations in the critical case

    Mat. Sb., 195:11 (2004),  31–62
  10. Asymptotics for Nonlinear Evolution Equations with Small Dissipation

    Differ. Uravn., 39:5 (2003),  624–637
  11. A Periodic Problem for the Landau–Ginzburg Equation

    Mat. Zametki, 72:2 (2002),  227–235
  12. Large time asymptotic behaviour of solutions of the complex Landau–Ginzburg equation

    Mat. Sb., 190:4 (1999),  95–114
  13. On the asymptotic behavior of solutions of the generalized Kolmogorov–Petrovskiǐ–Piskunov equation for large time values

    Differ. Uravn., 34:5 (1998),  668–681
  14. On an estimate for the eigenfunctions of a nonlinear operator

    Dokl. Akad. Nauk, 353:6 (1997),  730–733
  15. A periodic problem for a system of equations describing the conductivity of nerve pulses

    Differ. Uravn., 32:4 (1996),  562–564
  16. Asymptotics as $t\to\infty$ of the solutions of nonlinear equations with nonsmall initial perturbations

    Mat. Zametki, 59:6 (1996),  855–864
  17. Asymptotic behaviour as $t\to \infty$ of the solutions of the generalized Korteweg–de Vries equation

    Mat. Sb., 187:5 (1996),  71–110
  18. On the asymptotic behavior as $t\to\infty$ of the solutions of the generalized Kortweg–de Vries equation

    Dokl. Akad. Nauk, 344:2 (1995),  165–167
  19. On an asymptotic representation of surface waves in the form of two Burgers traveling waves

    Dokl. Akad. Nauk, 340:5 (1995),  602–606
  20. Asymptotic Representation of Surface Waves in the Form of Two Traveling Burgers Waves

    Funktsional. Anal. i Prilozhen., 29:3 (1995),  25–40
  21. On a relation between solutions of different nonlinear equations for large time values

    Dokl. Akad. Nauk, 334:4 (1994),  429–432
  22. An asymptotic relationship between solutions of different nonlinear equations for large time values. II

    Differ. Uravn., 30:8 (1994),  1432–1444
  23. An asymptotic relationship between solutions of different nonlinear equations for large time values. I

    Differ. Uravn., 30:5 (1994),  873–881
  24. On a system of equations that describes nerve conduction

    Dokl. Akad. Nauk, 328:6 (1993),  683–685
  25. A periodic problem for a nonlinear nonlocal Schrödinger equation

    Differ. Uravn., 29:11 (1993),  1996–1998
  26. Asymptotic behavior, for large time values, of the solutions of the Korteweg–de Vries equation with dissipation

    Differ. Uravn., 29:2 (1993),  306–319
  27. Asymptotic, as $t\to\infty$, of the solution of a nonlinear equation with weak dissipation and dispersion

    Izv. RAN. Ser. Mat., 57:6 (1993),  52–63
  28. On the stability of solutions of traveling wave type for the Kuramoto–Sivashinskii equation

    Dokl. Akad. Nauk, 323:2 (1992),  266–269
  29. On the destruction of surface waves

    Differ. Uravn., 28:5 (1992),  886–892
  30. Generalized solutions for the Whitham equation

    Differ. Uravn., 28:1 (1992),  121–126
  31. О распаде ступеньки для уравнения Кортевега–де Фриза–Бюргерса

    Funktsional. Anal. i Prilozhen., 26:2 (1992),  88–93
  32. On the asymptotic behavior as $t\to\infty$ of solutions of some nonlinear equations

    Dokl. Akad. Nauk SSSR, 321:2 (1991),  290–293
  33. The step-decay problem for the Korteweg-de Vries-Burgers equation

    Funktsional. Anal. i Prilozhen., 25:1 (1991),  21–32
  34. Asymptotic for large time of solutions of a system of equations for surface waves

    Izv. Akad. Nauk SSSR Ser. Mat., 55:3 (1991),  537–559
  35. The asymptotics as $t\to\infty$ of solutions of a nonlinear nonlocal Schrödinger equation

    Mat. Sb., 182:7 (1991),  1024–1042
  36. On the asymptotic behavior for large time values of solutions of a system of equations of surface waves

    Dokl. Akad. Nauk SSSR, 315:6 (1990),  1357–1360
  37. On a system of equations describing surface waves

    Izv. Akad. Nauk SSSR Ser. Mat., 54:4 (1990),  774–809
  38. The Cauchy problem for the Whitham equation. II

    Mat. Model., 2:9 (1990),  88–104
  39. The Cauchy problem for Whitham equation. I

    Mat. Model., 2:9 (1990),  70–87
  40. Asymptotic behavior of the solutions of the Whithem's equation for large time

    Mat. Model., 2:3 (1990),  75–88
  41. Asymptotic for $t\to\infty$ of solutions to generalized Kolmogorov–Vlasov–Piskunov equation

    Mat. Model., 1:6 (1989),  109–125
  42. Asymptotic behavior, as $t\to\infty,$ of solutions of nonlinear evolution equations with dissipation

    Mat. Zametki, 45:4 (1989),  118–121
  43. On the smoothing of solutions of the Cauchy problem for a system of equations of surface waves

    Mat. Zametki, 45:1 (1989),  136–138
  44. A periodic problem for Whitham's equation

    Mat. Sb., 180:7 (1989),  946–968
  45. A system of equations of surface waves

    Dokl. Akad. Nauk SSSR, 301:4 (1988),  788–793
  46. A periodic problem for the Whitham equation

    Dokl. Akad. Nauk SSSR, 299:5 (1988),  1063–1065
  47. Periodic solutions of partial differential equations with small parameters

    Differ. Uravn., 24:7 (1988),  1276–1278
  48. On the existence and destruction of waves that can be described by the Whitham equation

    Dokl. Akad. Nauk SSSR, 288:1 (1986),  90–95
  49. The Whitham equation with a singular kernel and small interaction

    Differ. Uravn., 21:10 (1985),  1818–1819
  50. Breaking of waves for the Whitham equation with singular kernel. II

    Differ. Uravn., 21:10 (1985),  1775–1790
  51. Breaking of waves for the Whitham equation with singular kernel. I

    Differ. Uravn., 21:3 (1985),  499–508
  52. On the Cauchy problem for the Whitham equation

    Dokl. Akad. Nauk SSSR, 273:4 (1983),  804–807
  53. On the breaking of waves for the Whitham equation

    Dokl. Akad. Nauk SSSR, 265:4 (1982),  809–811
  54. On the Cauchy problem and $T$-products for hypoelliptic systems

    Izv. Akad. Nauk SSSR Ser. Mat., 46:3 (1982),  617–649
  55. The Cauchy problem for hypoelliptic systems and representation of the interaction

    Differ. Uravn., 15:7 (1979),  1337–1339
  56. $T$-product of hypoelliptic operators

    Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 8 (1977),  137–197
  57. On asymptotic behavior as $t\to0$ and $T$-product for hypoelliptic systems

    Dokl. Akad. Nauk SSSR, 226:5 (1976),  1018–1020
  58. Analytic continuation of the Dirichlet series of elliptic boundary value problems. I, II

    Differ. Uravn., 6:10 (1970),  1844–1850
  59. Analytic continuation of the Dirichlet series of elliptic boundary value problems. I, II

    Differ. Uravn., 6:9 (1970),  1652–1672
  60. Estimates exact in a closed domain of the eigenfunctions of the polyharmonic operator

    Uspekhi Mat. Nauk, 25:1(151) (1970),  203–204
  61. Fourier series in fundamental systems of functions of the polyharmonic operator

    Dokl. Akad. Nauk SSSR, 189:4 (1969),  707–709
  62. The eigenfunctions of the polyharmonic operator

    Dokl. Akad. Nauk SSSR, 186:4 (1969),  781–782
  63. A mean value theorem for a polyharmonic equation and its consequences

    Funktsional. Anal. i Prilozhen., 3:4 (1969),  69–76
  64. Dirichlet series for elliptic operators

    Dokl. Akad. Nauk SSSR, 182:6 (1968),  1280–1282
  65. Exact estimates of the eigenfunctions of the biharmonic operator

    Dokl. Akad. Nauk SSSR, 170:4 (1966),  790–793
  66. Smoothness properties of generalized potentials of an elliptic operator

    Dokl. Akad. Nauk SSSR, 141:3 (1961),  547–550
  67. Uniform estimates of the derivatives of the solutions of the Dirichlet and eigenfunction problems for the operator $Lu=\operatorname{div}(p(x)\operatorname{grad}u)+q(x)\cdot u$ with discontinuous coefficients

    Dokl. Akad. Nauk SSSR, 137:1 (1961),  45–47
  68. An eigenfunction problem for the operator $Lu=\operatorname{div}[p(x)\operatorname{grad}u]-q(x)u$ with discontinuous coefficients

    Sibirsk. Mat. Zh., 2:4 (1961),  520–536
  69. The method of potentials for the problems of Dirichlet and Neumann in the case of equations with discontinuous coefficients

    Sibirsk. Mat. Zh., 2:1 (1961),  46–58
  70. Some problems for the $Lu=\operatorname{div}[p(x)\operatorname{grad}u]-q(x)u$ operator with discontinuous coefficients

    Dokl. Akad. Nauk SSSR, 135:4 (1960),  775–778
  71. A priori estimation of solutions to the Dirichlet problem for an elliptic operator with discontinuous coefficients

    Dokl. Akad. Nauk SSSR, 131:2 (1960),  269–272
  72. Uniform estimates in closed regions for the eigenfunctions of an elliptic operator and their derivatives

    Izv. Akad. Nauk SSSR Ser. Mat., 24:6 (1960),  883–896
  73. On the equivalence of the systems of generalized and classical eigenfunctions

    Izv. Akad. Nauk SSSR Ser. Mat., 24:5 (1960),  757–774
  74. The connection between generalized and classical solutions of the Dirichlet problem

    Izv. Akad. Nauk SSSR Ser. Mat., 24:4 (1960),  521–530

  75. Vladimir Aleksandrovich Il'in (on his 80th birthday)

    Uspekhi Mat. Nauk, 63:6(384) (2008),  173–182

© Steklov Math. Inst. of RAS, 2025