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Kornev, Andrey Alekseevich

Statistics Math-Net.Ru
Total publications: 19
Scientific articles: 19
Presentations: 2

Number of views:
This page:1073
Abstract pages:2116
Full texts:616
References:363
Professor
Doctor of physico-mathematical sciences (1995)
Speciality: 01.01.07 (Computing mathematics)
Birth date: 28.11.1969
E-mail: ;
Keywords: numerical analysis, globally stable approximation schemes, approximation attractor of a semidynamical system, numerical methods for a plasmas dynamics.

Subject:

1991–1996: numerical methods and differential theorems for the new mathematical models for Steady Self-focusing of Electromagnetic Beams in Plasma. 1996–present: an approach to verify continuity of a global attractor of a semidynamical system with a parameter is presented. This approach makes it possible to establish a connection between upper and lower semicontinuity of a global attractor and boundedness as a function of rate of attraction to a attractor. An approach to approximate a global attractor of a semidynamical system with error estimates in Hausdorff metric is studied. This approach is based on the properties of a function of rate of attraction to an attractor and on some new results for an unstable manifold in a neighborhood of an essential nonhyperbolical point.

Biography

EDUCATION 1986–1991: received the diploma with honour in mathematics (equivalent to the B. S. degree and M. S. degree) from the Moscow State University, the Department of Mathematics and Mechanics, Moscow, USSR (1991). 1991–1995: after post-graduate studies received the Candidate of Science degree in physics and mathematics under the thesis "Analysis the problem of a steady self-focusing of electromagnetic beams in plasma with allowance for relativistic and striction nonlinearities" in 1995. EMPLOYMENT 1991–present: the Department of Mathematics and Mechanics, Moscow State University, the Sub-faculty of Numerical Mathematics (1991, junior sci. researcher; 1999, assistant professor). A list of my works contains 15 titles.

   
Main publications:
  • Kornev A. A. On the peculiarity of the focus type in the solutions of a self-focusing problem with allowance for relativistic and striction nonlinearities // Russian J. Numer. Anal. Math. Modelling, 1997, 12(5), 436–442.

http://www.mathnet.ru/eng/person11232
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/628121

Publications in Math-Net.Ru
2019
1. K. A. Zhukov, A. A. Kornev, M. A. Lozhnikov, A. V. Popov, “Acceleration of transition to stationary mode for solutions to a system of viscous gas dynamics”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, 2,  14–21  mathnet; Moscow University Mathematics Bulletin, 74:2 (2019), 55–61  isi  scopus
2018
2. A. A. Kornev, “On some properties of the projection operator for a class of stabilization algorithms”, Vychisl. Metody Programm., 19:4 (2018),  431–438  mathnet
3. K. A. Zhukov, A. A. Kornev, A. V. Popov, “Acceleration of the process of entering stationary mode for molutions of a linearized system of viscous gas dynamics. II”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, 3,  3–8  mathnet; Moscow University Mathematics Bulletin, 73:3 (2018), 85–89  isi  scopus
4. K. A. Zhukov, A. A. Kornev, A. V. Popov, “Acceleration of transition to stationary state for solutions to a linearized viscous gas dynamics system. I”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, 1,  26–32  mathnet; Moscow University Mathematics Bulletin, 73:1 (2018), 24–29  isi  scopus
2017
5. A. A. Kornev, “Modeling the stabilization process on the boundary conditions for the quasi-two-dimensional fluid with the four vortex structure”, Matem. Mod., 29:11 (2017),  99–110  mathnet  elib; Math. Models Comput. Simul., 10:3 (2018), 363–372  scopus
2016
6. A. A. Kornev, “Numerical stabilization from the boundary for solutions of a model one-dimensional of a model one-Dimensional RBMK reactor”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, 3,  20–24  mathnet  mathscinet; Moscow University Mathematics Bulletin, 71:3 (2016), 106–110  isi  scopus
2014
7. E. Yu. Vedernikova, A. A. Kornev, “To the problem of rod heating”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, 6,  10–16  mathnet  mathscinet; Moscow University Mathematics Bulletin, 69:6 (2014), 237–241  scopus
2013
8. A. A. Kornev, A. M. Stepin, “On Asymptotic Contractions”, Mat. Zametki, 94:2 (2013),  218–224  mathnet  mathscinet  zmath  elib; Math. Notes, 94:2 (2013), 214–219  isi  elib  scopus
9. E. Yu. Vedernikova, A. A. Kornev, “The structure of a stable manifold for fully implicit schemes”, Vychisl. Metody Programm., 14:1 (2013),  44–49  mathnet
2009
10. A. A. Ivanchikov, A. A. Kornev, A. V. Ozeritskii, “On a new approach to asymptotic stabilization problems”, Zh. Vychisl. Mat. Mat. Fiz., 49:12 (2009),  2167–2181  mathnet; Comput. Math. Math. Phys., 49:12 (2009), 2070–2084  isi  scopus
2007
11. A. A. Kornev, “A Method of Graph Transformation Type for Numerical Simulation of Invariant Manifolds”, Tr. Mat. Inst. Steklova, 256 (2007),  237–251  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 256 (2007), 223–237  elib  scopus
12. A. A. Kornev, A. V. Ozeritskii, “Numerical stability of one method of asymptotic stabilization”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2007, 1,  33–36  mathnet  mathscinet  zmath
2006
13. A. A. Kornev, “A method for the asymptotic stabilization to a given trajectory based on the initial data”, Zh. Vychisl. Mat. Mat. Fiz., 46:1 (2006),  37–51  mathnet  mathscinet  zmath  elib; Comput. Math. Math. Phys., 46:1 (2006), 34–48  elib  scopus
2005
14. A. A. Kornev, A. V. Ozeritskii, “On approximate projecting on a stable manifold”, Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005),  1580–1586  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 45:9 (2005), 1525–1530
2004
15. A. A. Kornev, “On an iterative method for the construction the Hadamard mustaches”, Zh. Vychisl. Mat. Mat. Fiz., 44:8 (2004),  1346–1355  mathnet  mathscinet  zmath  elib; Comput. Math. Math. Phys., 44:8 (2004), 1274–1283
2001
16. A. A. Kornev, “Approximation of attractors of semidynamical systems”, Mat. Sb., 192:10 (2001),  19–32  mathnet  mathscinet  zmath  elib; Sb. Math., 192:10 (2001), 1435–1450  isi  scopus
2000
17. A. A. Kornev, “On new a priori estimates for modified Navier–Stokes equations in domains with nonsmooth boundaries in three-dimensional space”, Fundam. Prikl. Mat., 6:4 (2000),  1121–1129  mathnet  mathscinet  zmath
18. A. A. Kornev, “On the approximation of attractors of semidynamical systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, 3,  24–28  mathnet  mathscinet  zmath
1995
19. A. A. Kornev, “On a solution of an initial-boundary value problem for a nonlinear equation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, 6,  100–102  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. Об ускорении выхода на стационар решений системы вязкого газ
A. A. Kornev, M. A. Lozhnikov
Differential equations, analysis and control: theory and applications
November 19, 2018 18:30
2. Теоретические и прикладные вопросы в обобщенной теореме Адамара–Перрона
A. A. Kornev
Seminar of the Department of Differential Equations, Steklov Mathematical Institute of RAS
May 11, 2005

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