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Pyatkov Sergey Grigor'evich

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Total publications: 33
Scientific articles: 32

Number of views:
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Abstract pages:4618
Full texts:1540
References:619
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 . — 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
1. Recovering of lower order coefficients in forward-backward parabolic equations
S. G. Pyatkov, E. S. Kvich
Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018),  23–29
2. Inverse problems of recovering the boundary data with integral overdetermination conditions
S. G. Pyatkov, M. A. Verzhbitskii
Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 10:2 (2018),  37–46
3. Inverse problems for mathematical models of quasistationary electromagnetic waves in anisotropic nonmetallic media with dispersion
S. G. Pyatkov, S. N. Shergin
Vestnik YuUrGU. Ser. Mat. Model. Progr., 11:1 (2018),  44–59
4. On the source function recovering in quazilinear parabolic problems with pointwise overdetermination conditions
S. G. Pyatkov, V. V. Rotko
Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 9:4 (2017),  19–26
5. Parameter identification and control in heat transfer processes
S. G. Pyatkov, O. V. Goncharenko
Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:2 (2017),  51–62
6. On some classes of inverse problems of recovering a source function
S. G. Pyatkov, E. I. Safonov
Mat. Tr., 19:1 (2016),  178–198
7. On determining the source function in heat and mass transfer problems under integral overdetermination conditions
S. G. Pyatkov, M. V. Uvarova
Sib. Zh. Ind. Mat., 19:4 (2016),  93–100
8. On some classes of inverse problems with overdetermination data on spatial manifolds
S. G. Pyatkov
Sibirsk. Mat. Zh., 57:5 (2016),  1114–1126
9. Recovering a source function in a one-dimensional parabolic equation with dead zones taking into account
S. G. Pyatkov, V. V. Rotko
Mathematical notes of NEFU, 23:4 (2016),  46–57
10. On some inverse problems of determining boundary regimes
M. A. Verzhbitskii, S. G. Pyatkov
Mathematical notes of NEFU, 23:2 (2016),  3–18
11. Inverse problems for some Sobolev-type mathematical models
S. G. Pyatkov, S. N. Shergin
Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:2 (2016),  75–89
12. On some mathematical models of filtration theory
S. G. Pyatkov, S. N. Shergin
Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:2 (2015),  105–116
13. On some inverse problems for a linearized system of heat and mass transfer
E. M. Korotkova, S. G. Pyatkov
Mat. Tr., 17:2 (2014),  142–162
14. On some classes of linear inverse problems for parabolic systems of equations
S. G. Pyatkov, E. I. Safonov
Sib. Èlektron. Mat. Izv., 11 (2014),  777–799
15. Some inverse problems for convection-diffusion equations
S. G. Pyatkov, E. I. Safonov
Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:4 (2014),  36–50
16. On an inverse problem for a parabolic equation with the Cauchy data on a part of the lateral boundary of a cylinder
S. G. Pyatkov, A. G. Borichevskaya
Sibirsk. Mat. Zh., 54:2 (2013),  436–449
17. Some Inverse Problems for Mathematical Models of Heat and Mass Transfer
S. G. Pyatkov, A. G. Borichevskaya
Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:4 (2013),  63–72
18. On some classes of coefficient inverse problems for parabolic systems of equations
S. G. Pyatkov, M. L. Samkov
Mat. Tr., 15:1 (2012),  155–177
19. On the existence of maximal semidefinite invariant subspaces for $J$-dissipative operators
S. G. Pyatkov
Mat. Sb., 203:2 (2012),  87–110
20. On some inverse problems for elliptic equations and systems
S. G. Pyatkov
Sib. Zh. Ind. Mat., 13:4 (2010),  83–96
21. Some classes of inverse evolution problems for parabolic equations
S. G. Pyatkov, B. N. Tsybikov
Sibirsk. Mat. Zh., 50:1 (2009),  175–189
22. Certain inverse problems for parabolic equations
S. G. Pyatkov
Fundam. Prikl. Mat., 12:4 (2006),  187–202
23. Solvability of a certain boundary value problem for pseudoparabolic equations of the forth order
S. G. Pyatkov
Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 5:3 (2005),  43–56
24. Boundary Value Problems for Some Classes of Singular Parabolic Equations
S. G. Pyatkov
Mat. Tr., 6:2 (2003),  144–208
25. Solvability of boundary value problems for operator-differential equations of mixed type: the degenerate case
S. G. Pyatkov, N. L. Abasheieva
Sibirsk. Mat. Zh., 43:3 (2002),  678–693
26. Elliptic Eigenvalue Problems Involving an Indefinite Weight Function
S. G. Pyatkov
Mat. Tr., 4:2 (2001),  138–154
27. Interpolation of Weighted Sobolev Spaces
S. G. Pyatkov
Mat. Tr., 4:1 (2001),  122–173
28. Solvability of boundary value problems for operator-differential equations of mixed type
S. G. Pyatkov, N. L. Abasheieva
Sibirsk. Mat. Zh., 41:6 (2000),  1419–1435
29. Indefinite elliptic spectral problems
S. G. Pyatkov
Sibirsk. Mat. Zh., 39:2 (1998),  409–426
30. Riesz completeness of the eigenelements and associated elements of linear selfadjoint pencils
S. G. Pyatkov
Mat. Sb., 185:3 (1994),  93–116
31. Certain properties of eigenfunctions of linear pencils
S. G. Pyatkov
Mat. Zametki, 51:1 (1992),  141–148
32. An equation of composite type
S. G. Pyatkov
Differ. Uravn., 16:1 (1980),  117–123

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

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