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Pyatkov, Sergey Grigor'evich

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Total publications: 38
Scientific articles: 37

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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 г. — 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.

http://www.mathnet.ru/eng/person17679
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:pyatkov.sergei-g
https://mathscinet.ams.org/mathscinet/MRAuthorID/228632

Publications in Math-Net.Ru
2019
1. S. G. Pyatkov, V. V. Rotko, “Обратные задачи для некоторых квазилинейных параболических систем с точечными условиями переопределения”, Mat. Tr., 22:1 (2019),  178–204  mathnet
2. S. G. Pyatkov, “On Some Classes of Nonlocal Boundary-Value Problems for Singular Parabolic Equations”, Mat. Zametki, 106:4 (2019),  578–594  mathnet  elib; Math. Notes, 106:4 (2019), 602–615  isi  scopus
3. 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
4. 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
2018
5. 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
6. 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
7. 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
8. 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
9. 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
2016
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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
2015
16. 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
2014
17. 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
18. 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
19. 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
2013
20. 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
21. 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
2012
22. 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
23. 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
2010
24. 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
2009
25. 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
2006
26. 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
2005
27. 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
28. 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
2002
29. 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
2001
30. 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
31. 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
2000
32. 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
1998
33. 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
1994
34. 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
1992
35. 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
1985
36. 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
1980
37. S. G. Pyatkov, “An equation of composite type”, Differ. Uravn., 16:1 (1980),  117–123  mathnet  mathscinet  zmath

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

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