Persons
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
 
Pyatkov, Sergey Grigor'evich

Statistics Math-Net.Ru
Total publications: 66
Scientific articles: 65

Number of views:
This page:5524
Abstract pages:15896
Full texts:5343
References:2404
Professor
Doctor of physico-mathematical sciences (1995)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 5.01.1956
E-mail: , ,
Keywords: spectral theory of differential operators; elliptic eigenvalue problems with an indefinite weight function; weighted Sobolev spaces; boundary value problems for linear and nonlinear differential equations and systems; boundary value problems for operator-differential equations; operator theory.

Subject:

Necessary and sufficient and some sufficent conditions ensuring the Riesz basis property are obtained for the eigenfunctions and associated functions of the eigenvalue problems $Lu=\lambda Bu$, $x\in G\subset R^n$, $B_j u|_{\Gamma}=0$, $j=\overline{1,m}$, where $L$ is an elliptic, degenerate elliptic, or quasielliptic operator defined on a domain $G\subset R^n$ with boundary $\Gamma$, $B_j$'s are differential operators defined on $\Gamma$, and $Bu=g(x)u$, with $g(x)$ a measurable function assuming both positive and negative values in $G$. The basisness questions are studied in the weighted Lebesgue space endowed with the norm $\|u\|=\|u |g|^{1/2}\|_{L_{2}(G)}$. Similar results on the Riesz basis property are obtained for eigenelements and associated elements of linear selfadjoint pencils $Lu=\lambda Bu$. The questions of solvability of boundary value problems and qualitative properties of solutions are studied for the first order operator-differential equations $L(t)u=B(t)u_t$, where the operators $B(t):E\to E$ ($E$ is a complex Hilbert space) are symmetric at the interior points of the interval $(0,T)$ and selfadjoint at the points $0,T$, the operators $L(t)$ meet some conditions of the dissipativity type. The question on the interpolation is studied for the weighted Sobolev spaces endowed with the norm $\|u\|_{H_{p,\Psi}^m(\Omega)}^p= \int\limits_{\Omega}\sum\limits_{|\alpha|\le m}\omega_{\alpha}|D^{\alpha}u(x)|^p\,dx$. Here $\Psi=\{\omega_{\alpha}\}_{|\alpha|\le m}$ is a collection of positive continuous functions in $\Omega$. Under some conditions on $\omega_{\alpha}$, the spaces $(H_{p,\Psi}^m(\Omega),L_{p,\omega}(\Omega))_{1-s,p}$ are described ($\omega$ is also positive and continuous).

Biography

Data of birth: January 5, 1956 (Altai region, Russia). 1973–197 — Department of Mathematics, Novosibirsk State University (Novosibirsk).

1978–1980 — Probationer-researcher, Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences (Novosibirsk).

1982 ã. — Candidate of Physical and Mathematical Sciences (Ph.D.), Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences (Novosibirsk), Ph.D. Thesis "Well-posed boundary value problems for composite type equations and their generalizations".

1995 — Doctor of Physical and Mathematical Sciences (D.Sc.), Novosibirsk State University (Novosibirsk), D.Sc. Thesis "Indefinite spectral problems and their applications to the theory of boundary value problems of mathematical physics".

2002–present — Ugra State University, the head of the chair of mathematics.

   
Main publications:
  • Egorov I. E., Pyatkov S. G., Popov S. V. Neklassicheskie operatorno-differentsialnye uravneniya. Novosibirsk: Nauka, 2000.
  • Pyatkov S. G. Riesz completeness of the eigenelements and associated elements of linear selfadjoint pencils // Russian Acad. Sci. Sb. Math., v. 81, no. 2, 1995, p. 343–361.
  • Pyatkov S. G. Interpolation of weighted Sobolev spaces // Sib. Advan. Math., v. 10, no. 4, 2000, p. 83–132.
  • Pyatkov S. G., Abasheeva N. L. Razreshimost kraevykh zadach dlya operatorno-differentsialnykh uravnenii smeshannogo tipa // Sib. matem. zhurnal, t. 41, # 6, 2000, s. 1419–1435.
  • Pyatkov S. G. Elliptic eigenvalue problems involving an indefinite weight functions // Sib. Advan. Math., v. 10, no. 4, 2000, p. 134–150.

https://www.mathnet.ru/eng/person17679
List of publications on Google Scholar
https://zbmath.org/authors/ai:pyatkov.sergei-g
https://mathscinet.ams.org/mathscinet/MRAuthorID/228632
https://orcid.org/0000-0002-7238-9559

Publications in Math-Net.Ru Citations
2024
1. Egor I. Safonov, Sergey G. Pyatkov, Daniil A. Parunov, “Recovering surface fluxes on the boundary of the domain from pointwise measurements”, J. Sib. Fed. Univ. Math. Phys., 17:5 (2024),  632–643  mathnet
2. S. G. Pyatkov, O. A. Soldatov, “Identification of the heat transfer coefficient from boundary integral data”, Sibirsk. Mat. Zh., 65:4 (2024),  709–726  mathnet
3. E. I. Safonov, S. G. Pyatkov, “The flux recovering at the ecosystem-atmosphere boundary by inverse modelling”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 17:3 (2024),  29–45  mathnet
2023
4. S. G. Pyatkov, V. A. Belonogov, “Recovering of the heat transfer coefficient in transmission problems with imperfect contact conditions”, Chelyab. Fiz.-Mat. Zh., 8:3 (2023),  331–350  mathnet
5. S. G. Pyatkov, V. A. Baranchuk, “Determination of the Heat Transfer Coefficient in Mathematical Models of Heat and Mass Transfer”, Mat. Zametki, 113:1 (2023),  90–108  mathnet  mathscinet; Math. Notes, 113:1 (2023), 93–108  scopus 7
6. S. G. Pyatkov, O. I. Sokolkov, “On some classes of coefficient inverse problems of recovering thermophysical parameters in stratified media”, Mathematical notes of NEFU, 30:2 (2023),  56–74  mathnet
7. S. G. Pyatkov, O. A. Soldatov, “On some classes of inverse parabolic problems of recovering the thermophysical parameters”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 15:3 (2023),  23–33  mathnet
8. S. N. Shergin, S. G. Pyatkov, “Recovering of the heat transfer coefficient from the temperature measurements”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 16:3 (2023),  51–64  mathnet
2022
9. S. G. Pyatkov, V. A. Baranchuk, “Identification of a boundary condition in the heat and mass transfer problems”, Chelyab. Fiz.-Mat. Zh., 7:2 (2022),  234–253  mathnet  mathscinet 1
10. S. G. Pyatkov, “Identification of thermophysical parameters in mathematical models of heat and mass transfer”, J. Comp. Eng. Math., 9:2 (2022),  52–66  mathnet 2
11. V. A. Belonogov, S. G. Pyatkov, “On some classes of inverse problems of recovering the heat transfer coefficient in stratified media”, Sibirsk. Mat. Zh., 63:2 (2022),  252–271  mathnet; Siberian Math. J., 63:2 (2022), 206–223 8
12. S. G. Pyatkov, L. V. Neustroeva, “On solvability of inverse problems of determining point sources”, Mathematical notes of NEFU, 29:2 (2022),  43–58  mathnet
13. S. G. Pyatkov, “Cauchy problem solvability with the data specified on the rectangle boundary for a one-dimensional parabolic equation”, Russian Journal of Cybernetics, 3:2 (2022),  40–46  mathnet 1
14. S. G. Pyatkov, “On inverse problems with pointwise overdetermination for mathematical models of heat and mass transfer”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 15:3 (2022),  34–50  mathnet
2021
15. Sergey G. Pyatkov, Vladislav A. Baranchuk, “On some inverse parabolic problems with pointwise overdetermination”, J. Sib. Fed. Univ. Math. Phys., 14:4 (2021),  463–474  mathnet  isi 4
16. V. A. Belonogov, S. G. Pyatkov, “On solvability of some classes of transmission problems in a cylindrical space domain”, Sib. Èlektron. Mat. Izv., 18:1 (2021),  176–206  mathnet  isi 3
17. S. G. Pyatkov, “Boundary value and inverse problems for some classes of nonclassical operator-differential equations”, Sibirsk. Mat. Zh., 62:3 (2021),  603–618  mathnet  elib; Siberian Math. J., 62:3 (2021), 489–502  isi  scopus 4
18. S. G. Pyatkov, D. S. Orlova, “On some inverse problems for the Black–Scholes equation”, Mathematical notes of NEFU, 28:3 (2021),  45–69  mathnet  elib
19. S. G. Pyatkov, “On evolutionary inverse problems for mathematical models of heat and mass transfer”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 14:1 (2021),  5–25  mathnet
2020
20. S. G. Pyatkov, “On some classes of inverse problems on determining source functions for heat and mass transfer systems”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 188 (2020),  23–42  mathnet
21. V. A. Belonogov, S. G. Pyatkov, “On solvability of conjugation problems with non-ideal contact conditions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 7,  18–32  mathnet; Russian Math. (Iz. VUZ), 64:7 (2020), 13–26  isi  scopus 11
22. S. Z. Djamalov, S. G. Pyatkov, “On some boundary value problems for multidimensional higher order equations of mixed type”, Sibirsk. Mat. Zh., 61:4 (2020),  777–795  mathnet  elib; Siberian Math. J., 61:4 (2020), 610–625  isi  scopus 3
23. S. G. Pyatkov, M. V. Uvarova, T. V. Pronkina, “Inverse problems for a quasilinear parabolic system with integral overdetermination conditions”, Mathematical notes of NEFU, 27:4 (2020),  43–59  mathnet  elib 1
24. L. V. Neustroeva, S. G. Pyatkov, “About some classes of reverse tasks on determining the source function”, Mathematical notes of NEFU, 27:1 (2020),  21–40  mathnet  elib
2019
25. S. G. Pyatkov, V. V. Rotko, “Inverse problems with pointwise overdetermination for some quasilinear parabolic systems”, Mat. Tr., 22:1 (2019),  178–204  mathnet; Siberian Adv. Math., 30:2 (2020), 124–142  scopus 8
26. S. G. Pyatkov, “On Some Classes of Nonlocal Boundary-Value Problems for Singular Parabolic Equations”, Mat. Zametki, 106:4 (2019),  578–594  mathnet  mathscinet  elib; Math. Notes, 106:4 (2019), 602–615  isi  scopus
27. S. G. Pyatkov, “On some inverse problems for first order operator-differential equations”, Sibirsk. Mat. Zh., 60:1 (2019),  183–193  mathnet  elib; Siberian Math. J., 60:1 (2019), 140–147  isi  scopus 6
28. M. V. Uvarova, S. G. Pyatkov, “Some boundary value problems for the Sobolev-type operator-differential equations”, Mathematical notes of NEFU, 26:3 (2019),  71–89  mathnet  elib
29. S. N. Shergin, E. I. Safonov, S. G. Pyatkov, “On some inverse coefficient problems with the pointwise overdetermination for mathematical models of filtration”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:1 (2019),  82–95  mathnet  elib 2
2018
30. S. Z. Djamalov, S. G. Pyatkov, “Some classes of inverse problems for mixed type equations of second order”, Mathematical notes of NEFU, 25:4 (2018),  3–14  mathnet  elib
31. S. G. Pyatkov, E. S. Kvich, “Recovering of lower order coefficients in forward-backward parabolic equations”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018),  23–29  mathnet  elib 1
32. S. G. Pyatkov, M. A. Verzhbitskii, “Inverse problems of recovering the boundary data with integral overdetermination conditions”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 10:2 (2018),  37–46  mathnet  elib
33. S. G. Pyatkov, S. N. Shergin, “Inverse problems for mathematical models of quasistationary electromagnetic waves in anisotropic nonmetallic media with dispersion”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 11:1 (2018),  44–59  mathnet  elib
2017
34. S. G. Pyatkov, V. V. Rotko, “On the source function recovering in quazilinear parabolic problems with pointwise overdetermination conditions”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 9:4 (2017),  19–26  mathnet  elib 2
35. S. G. Pyatkov, O. V. Goncharenko, “Parameter identification and control in heat transfer processes”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:2 (2017),  51–62  mathnet  isi  elib 1
2016
36. S. G. Pyatkov, E. I. Safonov, “On some classes of inverse problems of recovering a source function”, Mat. Tr., 19:1 (2016),  178–198  mathnet  mathscinet  elib; Siberian Adv. Math., 27:2 (2017), 119–132  scopus 3
37. S. G. Pyatkov, M. V. Uvarova, “On determining the source function in heat and mass transfer problems under integral overdetermination conditions”, Sib. Zh. Ind. Mat., 19:4 (2016),  93–100  mathnet  mathscinet  elib; J. Appl. Industr. Math., 10:4 (2016), 549–555  scopus 4
38. S. G. Pyatkov, “On some classes of inverse problems with overdetermination data on spatial manifolds”, Sibirsk. Mat. Zh., 57:5 (2016),  1114–1126  mathnet  elib; Siberian Math. J., 57:5 (2016), 870–880  isi  elib  scopus 7
39. S. G. Pyatkov, V. V. Rotko, “Recovering a source function in a one-dimensional parabolic equation with dead zones taking into account”, Mathematical notes of NEFU, 23:4 (2016),  46–57  mathnet  elib
40. M. A. Verzhbitskii, S. G. Pyatkov, “On some inverse problems of determining boundary regimes”, Mathematical notes of NEFU, 23:2 (2016),  3–18  mathnet  elib 3
41. S. G. Pyatkov, S. N. Shergin, “Inverse problems for some Sobolev-type mathematical models”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:2 (2016),  75–89  mathnet  isi  elib 1
2015
42. S. G. Pyatkov, S. N. Shergin, “On some mathematical models of filtration theory”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:2 (2015),  105–116  mathnet  isi  elib 4
2014
43. E. M. Korotkova, S. G. Pyatkov, “On some inverse problems for a linearized system of heat and mass transfer”, Mat. Tr., 17:2 (2014),  142–162  mathnet  mathscinet; Siberian Adv. Math., 25:2 (2015), 110–123 3
44. S. G. Pyatkov, E. I. Safonov, “On some classes of linear inverse problems for parabolic systems of equations”, Sib. Èlektron. Mat. Izv., 11 (2014),  777–799  mathnet 11
45. S. G. Pyatkov, E. I. Safonov, “Some inverse problems for convection-diffusion equations”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:4 (2014),  36–50  mathnet 2
2013
46. S. G. Pyatkov, A. G. Borichevskaya, “On an inverse problem for a parabolic equation with the Cauchy data on a part of the lateral boundary of a cylinder”, Sibirsk. Mat. Zh., 54:2 (2013),  436–449  mathnet  mathscinet; Siberian Math. J., 54:2 (2013), 341–352  isi  scopus
47. S. G. Pyatkov, A. G. Borichevskaya, “Some Inverse Problems for Mathematical Models of Heat and Mass Transfer”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:4 (2013),  63–72  mathnet 1
2012
48. S. G. Pyatkov, M. L. Samkov, “On some classes of coefficient inverse problems for parabolic systems of equations”, Mat. Tr., 15:1 (2012),  155–177  mathnet  mathscinet  elib; Siberian Adv. Math., 22:4 (2012), 287–302 24
49. S. G. Pyatkov, “On the existence of maximal semidefinite invariant subspaces for $J$-dissipative operators”, Mat. Sb., 203:2 (2012),  87–110  mathnet  mathscinet  zmath  elib; Sb. Math., 203:2 (2012), 234–256  isi  scopus 5
2010
50. S. G. Pyatkov, “On some inverse problems for elliptic equations and systems”, Sib. Zh. Ind. Mat., 13:4 (2010),  83–96  mathnet  mathscinet  elib; J. Appl. Industr. Math., 5:3 (2011), 417–430 6
2009
51. S. G. Pyatkov, B. N. Tsybikov, “Some classes of inverse evolution problems for parabolic equations”, Sibirsk. Mat. Zh., 50:1 (2009),  175–189  mathnet  mathscinet; Siberian Math. J., 50:1 (2009), 141–153  isi  scopus 4
2006
52. S. G. Pyatkov, “Certain inverse problems for parabolic equations”, Fundam. Prikl. Mat., 12:4 (2006),  187–202  mathnet  mathscinet  zmath  elib; J. Math. Sci., 150:5 (2008), 2422–2433  elib  scopus 4
2005
53. S. G. Pyatkov, “Solvability of a certain boundary value problem for pseudoparabolic equations of the forth order”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 5:3 (2005),  43–56  mathnet
2003
54. S. G. Pyatkov, “Boundary Value Problems for Some Classes of Singular Parabolic Equations”, Mat. Tr., 6:2 (2003),  144–208  mathnet  mathscinet  zmath  elib; Siberian Adv. Math., 14:3 (2004), 63–125 4
2002
55. S. G. Pyatkov, N. L. Abasheieva, “Solvability of boundary value problems for operator-differential equations of mixed type: the degenerate case”, Sibirsk. Mat. Zh., 43:3 (2002),  678–693  mathnet  mathscinet  zmath; Siberian Math. J., 43:3 (2002), 549–561  isi 7
2001
56. S. G. Pyatkov, “Elliptic Eigenvalue Problems Involving an Indefinite Weight Function”, Mat. Tr., 4:2 (2001),  138–154  mathnet  mathscinet  zmath  elib; Siberian Adv. Math., 10:4 (2000), 134–150 3
57. S. G. Pyatkov, “Interpolation of Weighted Sobolev Spaces”, Mat. Tr., 4:1 (2001),  122–173  mathnet  mathscinet  zmath  elib; Siberian Adv. Math., 10:3 (2000), 83–132 5
2000
58. S. G. Pyatkov, N. L. Abasheieva, “Solvability of boundary value problems for operator-differential equations of mixed type”, Sibirsk. Mat. Zh., 41:6 (2000),  1419–1435  mathnet  mathscinet  zmath; Siberian Math. J., 41:6 (2000), 1174–1187  isi 8
1998
59. S. G. Pyatkov, “Indefinite elliptic spectral problems”, Sibirsk. Mat. Zh., 39:2 (1998),  409–426  mathnet  mathscinet  zmath; Siberian Math. J., 39:2 (1998), 358–372  isi 10
1994
60. S. G. Pyatkov, “Riesz completeness of the eigenelements and associated elements of linear selfadjoint pencils”, Mat. Sb., 185:3 (1994),  93–116  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 81:2 (1995), 343–361  isi 5
1992
61. S. G. Pyatkov, “Certain properties of eigenfunctions of linear pencils”, Mat. Zametki, 51:1 (1992),  141–148  mathnet  mathscinet  zmath; Math. Notes, 51:1 (1992), 90–95  isi 8
1989
62. S. G. Pyatkov, “Some properties of eigenfunctions of linear pencils”, Sibirsk. Mat. Zh., 30:4 (1989),  111–124  mathnet  mathscinet  zmath; Siberian Math. J., 30:4 (1989), 587–597  isi 21
1987
63. S. G. Pyatkov, A. G. Podgaev, “On the solvability of a boundary value problem for a nonlinear parabolic equation with changing time direction”, Sibirsk. Mat. Zh., 28:3 (1987),  184–192  mathnet  mathscinet  zmath; Siberian Math. J., 28:3 (1987), 498–505  isi 1
1985
64. S. G. Pyatkov, “Solvability of a boundary value problem for a parabolic equation with changing time direction”, Dokl. Akad. Nauk SSSR, 285:6 (1985),  1327–1329  mathnet  mathscinet  zmath 7
1980
65. S. G. Pyatkov, “An equation of composite type”, Differ. Uravn., 16:1 (1980),  117–123  mathnet  mathscinet  zmath 1

2016
66. A. I. Kozhanov, S. G. Pyatkov, “Vragov Vladimir Nikolaevich”, Sib. J. Pure and Appl. Math., 16:2 (2016),  3–5  mathnet

Organisations
 
  Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024