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Naumkin, Pavel Ivanovich

Statistics Math-Net.Ru
Total publications: 55
Scientific articles: 55

Number of views:
This page:3142
Abstract pages:17071
Full texts:6528
References:1969
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Keywords: asymptotics in the far region, nonlinear heat equation, critical nonlinearity.

https://www.mathnet.ru/eng/person8435
List of publications on Google Scholar
https://zbmath.org/authors/ai:naumkin.pavel-i
https://mathscinet.ams.org/mathscinet/MRAuthorID/198726

Publications in Math-Net.Ru Citations
2023
1. P. I. Naumkin, “Logarithmic nature of the long-time asymptotics of solutions of a Sobolev-type nonlinear equations with cubic nonlinearities”, Mat. Sb., 214:7 (2023),  134–160  mathnet  mathscinet  zmath; Sb. Math., 214:7 (2023), 1024–1050  isi  scopus
2019
2. P. I. Naumkin, “Asymptotics of solutions of a modified Whitham equation with surface tension”, Izv. RAN. Ser. Mat., 83:2 (2019),  174–203  mathnet  mathscinet  zmath  elib; Izv. Math., 83:2 (2019), 361–390  isi  scopus 1
3. P. I. Naumkin, “Time decay estimates for solutions of the Cauchy problem for the modified Kawahara equation”, Mat. Sb., 210:5 (2019),  72–108  mathnet  mathscinet  zmath  elib; Sb. Math., 210:5 (2019), 693–730  isi  scopus 6
2015
4. P. I. Naumkin, “The dissipative property of a cubic non-linear Schrödinger equation”, Izv. RAN. Ser. Mat., 79:2 (2015),  137–166  mathnet  mathscinet  zmath  elib; Izv. Math., 79:2 (2015), 346–374  isi  scopus 10
2013
5. 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 4
2012
6. 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
7. 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 10
2009
8. 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
9. 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 6
2007
10. N. Hayashi, E. I. Kaikina, P. I. Naumkin, “Asymptotics for nonlinear damped wave equations with large initial data”, Sib. Èlektron. Mat. Izv., 4 (2007),  249–277  mathnet  mathscinet  zmath 3
2005
11. 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 45
2004
12. 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 3
13. 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 1
2003
14. 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
1997
15. P. I. Naumkin, “Evolution of a step for the Benjamin–Bona–Mahony–Burgers equation”, Dokl. Akad. Nauk, 352:6 (1997),  742–745  mathnet  mathscinet  zmath
16. P. I. Naumkin, “Solution asymptotics at large times for the non-linear Schrödinger equation”, Izv. RAN. Ser. Mat., 61:4 (1997),  81–118  mathnet  mathscinet  zmath; Izv. Math., 61:4 (1997), 757–794  isi  scopus 9
1996
17. 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
18. 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 12
19. 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 4
1995
20. P. I. Naumkin, I. A. Shishmarev, “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  mathnet  mathscinet  zmath
21. P. I. Naumkin, I. A. Shishmarev, “On an asymptotic representation of surface waves in the form of two Burgers traveling waves”, Dokl. Akad. Nauk, 340:5 (1995),  602–606  mathnet  mathscinet  zmath
22. 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 3
1994
23. P. I. Naumkin, I. A. Shishmarev, “On a relation between solutions of different nonlinear equations for large time values”, Dokl. Akad. Nauk, 334:4 (1994),  429–432  mathnet  mathscinet  zmath; Dokl. Math., 49:1 (1994), 127–131
24. 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
25. 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 1
1993
26. P. I. Naumkin, I. A. Shishmarev, “On a system of equations that describes nerve conduction”, Dokl. Akad. Nauk, 328:6 (1993),  683–685  mathnet  mathscinet  zmath; Dokl. Math., 38:2 (1993), 69–70
27. P. I. Naumkin, “On the asymptotic behavior for large time values of the solutions of nonlinear equations in the case of maximal order”, Differ. Uravn., 29:6 (1993),  1071–1074  mathnet  mathscinet; Differ. Equ., 29:6 (1993), 926–929
28. 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
29. 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 1
30. P. I. Naumkin, “Large-time asymptotic of solutions of the nonlinear Schrodinger equation in $2+1$ dimensions”, Izv. RAN. Ser. Mat., 57:5 (1993),  197–209  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 43:2 (1994), 373–384  isi 2
1992
31. P. I. Naumkin, I. A. Shishmarev, “On the stability of solutions of traveling wave type for the Kuramoto–Sivashinskii equation”, Dokl. Akad. Nauk, 323:2 (1992),  266–269  mathnet  mathscinet; Dokl. Math., 37:3 (1992), 129–130
32. 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 1
33. 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
34. 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 3
1991
35. P. I. Naumkin, I. A. Shishmarev, “On the asymptotic behavior as $t\to\infty$ of solutions of some nonlinear equations”, Dokl. Akad. Nauk SSSR, 321:2 (1991),  290–293  mathnet  mathscinet  zmath; Dokl. Math., 36:11 (1991), 755–756 1
36. 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 10
37. 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 4
38. 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 1
1990
39. P. I. Naumkin, I. A. Shishmarev, “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  mathnet  mathscinet  zmath; Dokl. Math., 35:12 (1990), 1039–1040
40. 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 2
41. P. I. Naumkin, I. A. Shishmarev, “The Cauchy problem for the Whitham equation. II”, Mat. Model., 2:9 (1990),  88–104  mathnet  mathscinet  zmath 1
42. P. I. Naumkin, I. A. Shishmarev, “The Cauchy problem for Whitham equation. I”, Mat. Model., 2:9 (1990),  70–87  mathnet  mathscinet  zmath 1
43. P. I. Naumkin, I. A. Shishmarev, “Asymptotic behavior of the solutions of the Whithem's equation for large time”, Mat. Model., 2:3 (1990),  75–88  mathnet  mathscinet  zmath 6
1989
44. P. I. Naumkin, I. A. Shishmarev, “Asymptotic for $t\to\infty$ of solutions to generalized Kolmogorov–Vlasov–Piskunov equation”, Mat. Model., 1:6 (1989),  109–125  mathnet  mathscinet  zmath 5
45. 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 5
46. 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 2
1988
47. P. I. Naumkin, I. A. Shishmarev, “A system of equations of surface waves”, Dokl. Akad. Nauk SSSR, 301:4 (1988),  788–793  mathnet  mathscinet  zmath; Dokl. Math., 38:1 (1989), 147–151 2
48. P. I. Naumkin, I. A. Shishmarev, “A periodic problem for the Whitham equation”, Dokl. Akad. Nauk SSSR, 299:5 (1988),  1063–1065  mathnet  mathscinet  zmath; Dokl. Math., 37:2 (1988), 526–528
1987
49. P. I. Naumkin, “Whitham's equation with a singular kernel”, Zh. Vychisl. Mat. Mat. Fiz., 27:4 (1987),  633–636  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 27:2 (1987), 209–211 1
1986
50. 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 1
1985
51. 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 1
52. 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 1
53. 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
54. 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
55. 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 1

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