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Shishmarev, Il'ya Andreevich
(1937–2012)

Statistics Math-Net.Ru
Total publications: 63
Scientific articles: 62

Number of views:
This page:785
Abstract pages:9913
Full texts:4231
References:819
Keywords: asymptotics in the far region, nonlinear heat equation, critical nonlinearity.

http://www.mathnet.ru/eng/person8436
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/198727

Publications in Math-Net.Ru
2013
1. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Asymptotic expansion of solutions to the periodic problem for a non-linear Sobolev-type equation”, Izv. RAN. Ser. Mat., 77:2 (2013),  97–108  mathnet  mathscinet  zmath  elib; Izv. Math., 77:2 (2013), 313–324  isi  elib  scopus
2012
2. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “The far-field asymptotics of solutions of a fractional non-linear equation”, Izv. RAN. Ser. Mat., 76:2 (2012),  37–66  mathnet  mathscinet  zmath  elib; Izv. Math., 76:2 (2012), 245–274  isi  elib  scopus
2010
3. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Periodic Boundary Value Problem for Nonlinear Sobolev-Type Equations”, Funktsional. Anal. i Prilozhen., 44:3 (2010),  14–26  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 44:3 (2010), 171–181  isi  scopus
2009
4. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “A boundary-value problem for a non-linear equation with a fractional derivative”, Izv. RAN. Ser. Mat., 73:6 (2009),  101–124  mathnet  mathscinet  zmath  elib; Izv. Math., 73:6 (2009), 1173–1196  isi  scopus
5. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations”, Uspekhi Mat. Nauk, 64:3(387) (2009),  3–72  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 64:3 (2009), 399–468  isi  elib  scopus
2005
6. I. A. Shishmarev, “On a nonlinear Sobolev type equation”, Differ. Uravn., 41:1 (2005),  138–140  mathnet  mathscinet; Differ. Equ., 41:1 (2005), 146–149
7. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “The Cauchy problem for an equation of Sobolev type with power non-linearity”, Izv. RAN. Ser. Mat., 69:1 (2005),  61–114  mathnet  mathscinet  zmath  elib; Izv. Math., 69:1 (2005), 59–111  isi  elib  scopus
2004
8. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Asymptotics of solutions of non-linear dissipative equations”, Izv. RAN. Ser. Mat., 68:3 (2004),  29–62  mathnet  mathscinet  zmath; Izv. Math., 68:3 (2004), 461–492  isi  scopus
9. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Cauchy problem for non-linear systems of equations in the critical case”, Mat. Sb., 195:11 (2004),  31–62  mathnet  mathscinet  zmath; Sb. Math., 195:11 (2004), 1575–1605  isi  scopus
2003
10. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Asymptotics for Nonlinear Evolution Equations with Small Dissipation”, Differ. Uravn., 39:5 (2003),  624–637  mathnet  mathscinet; Differ. Equ., 39:5 (2003), 658–673
2002
11. M. V. Komarov, I. A. Shishmarev, “A Periodic Problem for the Landau–Ginzburg Equation”, Mat. Zametki, 72:2 (2002),  227–235  mathnet  mathscinet  zmath; Math. Notes, 72:2 (2002), 204–211  isi  scopus
1999
12. I. A. Shishmarev, M. Tsutsumi, “Large time asymptotic behaviour of solutions of the complex Landau–Ginzburg equation”, Mat. Sb., 190:4 (1999),  95–114  mathnet  mathscinet  zmath; Sb. Math., 190:4 (1999), 569–588  isi  scopus
1998
13. V. V. Konotop, I. A. Shishmarev, “On the asymptotic behavior of solutions of the generalized Kolmogorov–Petrovskiǐ–Piskunov equation for large time values”, Differ. Uravn., 34:5 (1998),  668–681  mathnet  mathscinet; Differ. Equ., 34:5 (1998), 669–682
1996
14. P. I. Naumkin, I. A. Shishmarev, “A periodic problem for a system of equations describing the conductivity of nerve pulses”, Differ. Uravn., 32:4 (1996),  562–564  mathnet  mathscinet; Differ. Equ., 32:4 (1996), 568–570
15. P. I. Naumkin, I. A. Shishmarev, “Asymptotics as $t\to\infty$ of the solutions of nonlinear equations with nonsmall initial perturbations”, Mat. Zametki, 59:6 (1996),  855–864  mathnet  mathscinet  zmath; Math. Notes, 59:6 (1996), 618–624  isi
16. P. I. Naumkin, I. A. Shishmarev, “Asymptotic behaviour as $t\to \infty$ of the solutions of the generalized Korteweg–de Vries equation”, Mat. Sb., 187:5 (1996),  71–110  mathnet  mathscinet  zmath; Sb. Math., 187:5 (1996), 693–733  isi  scopus
1995
17. P. I. Naumkin, I. A. Shishmarev, “Asymptotic Representation of Surface Waves in the Form of Two Traveling Burgers Waves”, Funktsional. Anal. i Prilozhen., 29:3 (1995),  25–40  mathnet  mathscinet  zmath; Funct. Anal. Appl., 29:3 (1995), 168–179  isi
1994
18. P. I. Naumkin, I. A. Shishmarev, “An asymptotic relationship between solutions of different nonlinear equations for large time values. II”, Differ. Uravn., 30:8 (1994),  1432–1444  mathnet  mathscinet; Differ. Equ., 30:8 (1994), 1329–1340
19. P. I. Naumkin, I. A. Shishmarev, “An asymptotic relationship between solutions of different nonlinear equations for large time values. I”, Differ. Uravn., 30:5 (1994),  873–881  mathnet  mathscinet; Differ. Equ., 30:5 (1994), 806–814
1993
20. E. I. Kaikina, I. A. Shishmarev, “A periodic problem for a nonlinear nonlocal Schrödinger equation”, Differ. Uravn., 29:11 (1993),  1996–1998  mathnet  mathscinet; Differ. Equ., 29:11 (1993), 1733–1736
21. P. I. Naumkin, I. A. Shishmarev, “Asymptotic behavior, for large time values, of the solutions of the Korteweg–de Vries equation with dissipation”, Differ. Uravn., 29:2 (1993),  306–319  mathnet  mathscinet; Differ. Equ., 29:2 (1993), 253–263
22. P. I. Naumkin, I. A. Shishmarev, “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  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 43:3 (1994), 443–453  isi
1992
23. P. I. Naumkin, I. A. Shishmarev, “On the destruction of surface waves”, Differ. Uravn., 28:5 (1992),  886–892  mathnet  mathscinet; Differ. Equ., 28:5 (1992), 722–728
24. P. I. Naumkin, I. A. Shishmarev, “Generalized solutions for the Whitham equation”, Differ. Uravn., 28:1 (1992),  121–126  mathnet  mathscinet  zmath; Differ. Equ., 28:1 (1992), 115–120
25. P. I. Naumkin, I. A. Shishmarev, “О распаде ступеньки для уравнения Кортевега–де Фриза–Бюргерса”, Funktsional. Anal. i Prilozhen., 26:2 (1992),  88–93  mathnet  mathscinet  zmath
1991
26. P. I. Naumkin, I. A. Shishmarev, “The step-decay problem for the Korteweg-de Vries-Burgers equation”, Funktsional. Anal. i Prilozhen., 25:1 (1991),  21–32  mathnet  mathscinet  zmath; Funct. Anal. Appl., 25:1 (1991), 16–25  isi
27. P. I. Naumkin, I. A. Shishmarev, “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  mathnet  mathscinet  zmath; Math. USSR-Izv., 38:3 (1992), 525–551  isi
28. P. I. Naumkin, I. A. Shishmarev, “The asymptotics as $t\to\infty$ of solutions of a nonlinear nonlocal Schrödinger equation”, Mat. Sb., 182:7 (1991),  1024–1042  mathnet  mathscinet  zmath; Math. USSR-Sb., 73:2 (1992), 393–413  isi
1990
29. P. I. Naumkin, I. A. Shishmarev, “On a system of equations describing surface waves”, Izv. Akad. Nauk SSSR Ser. Mat., 54:4 (1990),  774–809  mathnet  mathscinet  zmath; Math. USSR-Izv., 37:1 (1991), 119–156
30. P. I. Naumkin, I. A. Shishmarev, “The Cauchy problem for the Whitham equation. II”, Matem. Mod., 2:9 (1990),  88–104  mathnet  mathscinet  zmath
31. P. I. Naumkin, I. A. Shishmarev, “The Cauchy problem for Whitham equation. I”, Matem. Mod., 2:9 (1990),  70–87  mathnet  mathscinet  zmath
32. P. I. Naumkin, I. A. Shishmarev, “Asymptotic behavior of the solutions of the Whithem's equation for large time”, Matem. Mod., 2:3 (1990),  75–88  mathnet  mathscinet  zmath
1989
33. P. I. Naumkin, I. A. Shishmarev, “Asymptotic for $t\to\infty$ of solutions to generalized Kolmogorov–Vlasov–Piskunov equation”, Matem. Mod., 1:6 (1989),  109–125  mathnet  mathscinet  zmath
34. P. I. Naumkin, I. A. Shishmarev, “Asymptotic behavior, as $t\to\infty,$ of solutions of nonlinear evolution equations with dissipation”, Mat. Zametki, 45:4 (1989),  118–121  mathnet  mathscinet  zmath
35. I. A. Shishmarev, “On the smoothing of solutions of the Cauchy problem for a system of equations of surface waves”, Mat. Zametki, 45:1 (1989),  136–138  mathnet  mathscinet  zmath
36. P. I. Naumkin, I. A. Shishmarev, “A periodic problem for Whitham's equation”, Mat. Sb., 180:7 (1989),  946–968  mathnet  mathscinet  zmath; Math. USSR-Sb., 67:2 (1990), 403–426  isi
1988
37. M. A. Petrova, I. A. Shishmarev, “Periodic solutions of partial differential equations with small parameters”, Differ. Uravn., 24:7 (1988),  1276–1278  mathnet  mathscinet  zmath
1986
38. P. I. Naumkin, I. A. Shishmarev, “On the existence and destruction of waves that can be described by the Whitham equation”, Dokl. Akad. Nauk SSSR, 288:1 (1986),  90–95  mathnet  mathscinet  zmath
1985
39. P. I. Naumkin, I. A. Shishmarev, “The Whitham equation with a singular kernel and small interaction”, Differ. Uravn., 21:10 (1985),  1818–1819  mathnet  mathscinet  zmath
40. P. I. Naumkin, I. A. Shishmarev, “Breaking of waves for the Whitham equation with singular kernel. II”, Differ. Uravn., 21:10 (1985),  1775–1790  mathnet  mathscinet  zmath
41. P. I. Naumkin, I. A. Shishmarev, “Breaking of waves for the Whitham equation with singular kernel. I”, Differ. Uravn., 21:3 (1985),  499–508  mathnet  mathscinet  zmath
1983
42. P. I. Naumkin, I. A. Shishmarev, “On the Cauchy problem for the Whitham equation”, Dokl. Akad. Nauk SSSR, 273:4 (1983),  804–807  mathnet  mathscinet  zmath
1982
43. P. I. Naumkin, I. A. Shishmarev, “On the breaking of waves for the Whitham equation”, Dokl. Akad. Nauk SSSR, 265:4 (1982),  809–811  mathnet  mathscinet  zmath
44. I. A. Shishmarev, “On the Cauchy problem and $T$-products for hypoelliptic systems”, Izv. Akad. Nauk SSSR Ser. Mat., 46:3 (1982),  617–649  mathnet  mathscinet  zmath; Math. USSR-Izv., 20:3 (1983), 577–609
1979
45. I. A. Shishmarev, “The Cauchy problem for hypoelliptic systems and representation of the interaction”, Differ. Uravn., 15:7 (1979),  1337–1339  mathnet  mathscinet  zmath
1977
46. V. P. Maslov, I. A. Shishmarev, “$T$-product of hypoelliptic operators”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 8 (1977),  137–197  mathnet  zmath; J. Soviet Math., 13:1 (1980), 81–118
1976
47. I. A. Shishmarev, “On asymptotic behavior as $t\to0$ and $T$-product for hypoelliptic systems”, Dokl. Akad. Nauk SSSR, 226:5 (1976),  1018–1020  mathnet
1970
48. V. E. Shatalov, I. A. Shishmarev, “Analytic continuation of the Dirichlet series of elliptic boundary value problems. I, II”, Differ. Uravn., 6:10 (1970),  1844–1850  mathnet  mathscinet  zmath
49. V. E. Shatalov, I. A. Shishmarev, “Analytic continuation of the Dirichlet series of elliptic boundary value problems. I, II”, Differ. Uravn., 6:9 (1970),  1652–1672  mathnet  mathscinet  zmath
50. I. A. Shishmarev, “Estimates exact in a closed domain of the eigenfunctions of the polyharmonic operator”, Uspekhi Mat. Nauk, 25:1(151) (1970),  203–204  mathnet  mathscinet  zmath
1969
51. V. A. Il'in, I. A. Shishmarev, “Fourier series in fundamental systems of functions of the polyharmonic operator”, Dokl. Akad. Nauk SSSR, 189:4 (1969),  707–709  mathnet  mathscinet
52. I. A. Shishmarev, “The eigenfunctions of the polyharmonic operator”, Dokl. Akad. Nauk SSSR, 186:4 (1969),  781–782  mathnet  mathscinet  zmath
53. I. A. Shishmarev, “A mean value theorem for a polyharmonic equation and its consequences”, Funktsional. Anal. i Prilozhen., 3:4 (1969),  69–76  mathnet  mathscinet  zmath; Funct. Anal. Appl., 3:4 (1969), 312–318
1968
54. V. E. Shatalov, I. A. Shishmarev, “Dirichlet series for elliptic operators”, Dokl. Akad. Nauk SSSR, 182:6 (1968),  1280–1282  mathnet  mathscinet  zmath
1966
55. I. A. Shishmarev, “Exact estimates of the eigenfunctions of the biharmonic operator”, Dokl. Akad. Nauk SSSR, 170:4 (1966),  790–793  mathnet  mathscinet  zmath
1961
56. V. A. Il'in, I. A. Shishmarev, “Smoothness properties of generalized potentials of an elliptic operator”, Dokl. Akad. Nauk SSSR, 141:3 (1961),  547–550  mathnet  mathscinet  zmath
57. I. A. Shishmarev, “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  mathnet  mathscinet  zmath
1960
58. V. A. Il'in, I. A. Shishmarev, “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  mathnet  mathscinet  zmath
59. I. A. Shishmarev, “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  mathnet  mathscinet  zmath
60. V. A. Il'in, I. A. Shishmarev, “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  mathnet  mathscinet  zmath
61. V. A. Il'in, I. A. Shishmarev, “On the equivalence of the systems of generalized and classical eigenfunctions”, Izv. Akad. Nauk SSSR Ser. Mat., 24:5 (1960),  757–774  mathnet  mathscinet  zmath
62. V. A. Il'in, I. A. Shishmarev, “The connection between generalized and classical solutions of the Dirichlet problem”, Izv. Akad. Nauk SSSR Ser. Mat., 24:4 (1960),  521–530  mathnet  mathscinet  zmath

2008
63. O. M. Belotserkovskii, I. S. Lomov, E. I. Moiseev, Yu. S. Osipov, V. A. Sadovnichii, I. A. Shishmarev, “Vladimir Aleksandrovich Il'in (on his 80th birthday)”, Uspekhi Mat. Nauk, 63:6(384) (2008),  173–182  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:6 (2008), 1163–1172  isi

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