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Ilyin, Aleksei Andreevich

Statistics Math-Net.Ru
Total publications: 37
Scientific articles: 37
Presentations: 9

Number of views:
This page:1494
Abstract pages:7321
Full texts:2102
References:741
Senior Researcher
Doctor of physico-mathematical sciences (2006)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
   
Main publications:
  • A. A. Ilyin, Attractors for Navier–Stokes equations in domains with finite measure, Nonlinear Analysis, 27:5 (1996), 605–616.
  • A. A. Ilyin, Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides, Mat. Sbornik, 187:5 (1996), 15–58.
  • A. A. Ilyin, Best constants in a class of polymultiplicative inequalities for derivatives, Mat. Sbornik, 189:9 (1998), 15–58.
  • V. V. Chepyzhov, A. A. Ilyin, On the fractal dimension of invariant sets applications to the Navier–Stokes equations, Discrete and Continuous Dynamical Systems, 10 (2004), 117–135.
  • A. A. Ilyin, Lieb–Thirring integral inequalities and their applications to the attractors of the Navier–Stokes equations, Mat. Sbornik, 196:1 (2005), 3–66.

http://www.mathnet.ru/eng/person8620
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/221381

Publications in Math-Net.Ru
2020
1. A. A. Ilyin, A. A. Laptev, “Magnetic Lieb–Thirring inequality for periodic functions”, Uspekhi Mat. Nauk, 75:4(454) (2020),  207–208  mathnet; Russian Math. Surveys, 75:4 (2020), 779–781  isi  scopus
2019
2. A. Ilyin, A. Laptev, “Lieb–Thirring inequalities on the sphere”, Algebra i Analiz, 31:3 (2019),  116–135  mathnet
3. S. V. Zelik, A. A. Ilyin, A. A. Laptev, “On the Lieb–Thirring Constant on the Torus”, Mat. Zametki, 106:6 (2019),  946–950  mathnet  elib; Math. Notes, 106:6 (2019), 1020–1024  isi  scopus
2017
4. A. A. Ilyin, V. V. Chepyzhov, “On Strong Convergence of Attractors of Navier–Stokes Equations in the Limit of Vanishing Viscosity”, Mat. Zametki, 101:4 (2017),  635–639  mathnet  mathscinet  elib; Math. Notes, 101:4 (2017), 746–750  isi  scopus
2016
5. A. A. Ilyin, Yu. G. Rykov, “On the closeness of trajectories for model quasi-gasdynamic equations. Linear case”, Keldysh Institute preprints, 2016, 090, 14 pp.  mathnet
6. A. A. Ilyin, A. A. Laptev, “Lieb-Thirring inequalities on the torus”, Mat. Sb., 207:10 (2016),  56–79  mathnet  mathscinet  elib; Sb. Math., 207:10 (2016), 1410–1434  isi  scopus
2014
7. S. V. Zelik, A. A. Ilyin, “Green's function asymptotics and sharp interpolation inequalities”, Uspekhi Mat. Nauk, 69:2(416) (2014),  23–76  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 69:2 (2014), 209–260  isi  scopus
8. A. A. Ilyin, “A class of sharp inequalities for periodic functions. Addendum to the paper “Smooth solutions of the Navier-Stokes equations” by S. I. Pokhozhaev”, Mat. Sb., 205:2 (2014),  71–74  mathnet  mathscinet  zmath  elib; Sb. Math., 205:2 (2014), 220–223  isi  elib  scopus
2013
9. A. A. Ilyin, “Lower bounds for sums of eigenvalues of elliptic operators and systems”, Mat. Sb., 204:4 (2013),  103–126  mathnet  mathscinet  zmath  elib; Sb. Math., 204:4 (2013), 563–587  isi  scopus
2012
10. A. A. Ilyin, Yu. G. Rykov, “On a model system with a small parameter as a coefficient of the highest time derivative arising in the analysis of certain quasihydrodymamical systems”, Keldysh Institute preprints, 2012, 075, 9 pp.  mathnet
11. A. A. Ilyin, Yu. G. Rykov, “On a model equation with small parameter as a coefficient of the second-order time derivative arising in the analysis of certain quasi-gasdynamics systems”, Keldysh Institute preprints, 2012, 012, 9 pp.  mathnet
2009
12. A. A. Ilyin, “On the Spectrum of the Stokes Operator”, Funktsional. Anal. i Prilozhen., 43:4 (2009),  14–25  mathnet  mathscinet  zmath; Funct. Anal. Appl., 43:4 (2009), 254–263  isi
2006
13. A. A. Ilyin, N. V. Kupriyanova, M. Yu. Ovchinnikov, V. I. Pen'kov, A. S. Selivanov, “Attitude dynamics analysis of the first Russian nanosatellite TNS-0 using flight test results”, Keldysh Institute preprints, 2006, 018, 28 pp.  mathnet
14. A. A. Ilyin, “Lieb–Thirring Integral Inequalities and Sharp Bounds for the Dimension of the Attractor of the Navier–Stokes Equations with Friction”, Tr. Mat. Inst. Steklova, 255 (2006),  146–160  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 255 (2006), 136–149  scopus
2005
15. A. A. Ilyin, M. Yu. Ovchinnikov, V. I. Pen'kov, “Algorithms of the magnetic attitude control system for the small spin-stabilized satellite”, Keldysh Institute preprints, 2005, 019, 32 pp.  mathnet
16. A. A. Ilyin, “Lieb–Thirring integral inequalities and their applications to attractors of the Navier–Stokes equations”, Mat. Sb., 196:1 (2005),  33–66  mathnet  mathscinet  zmath  elib; Sb. Math., 196:1 (2005), 29–61  isi  elib  scopus
2004
17. A. A. Ilyin, M. Yu. Ovchinnikov, V. I. Pen'kov, “Orientation maintenance of a small spin-stabilized satellite”, Keldysh Institute preprints, 2004, 083, 26 pp.  mathnet
18. A. A. Belov, P. Behr, D. V. Vorontsov, B. V. Zubkov, A. A. Ilyin, A. P. Kalinin, S. Montenegro, A. M. Ovchinnikov, M. Yu. Ovchinnikov, A. G. Orlov, A. N. Ostanniy, S. Pletner, I. V. Ritus, A. I. Rodionov, I. D. Rodionov, I. P. Rodionova, E. Yu. Fedunin, “Distributed on-board computer system prototype”, Keldysh Institute preprints, 2004, 025, 22 pp.  mathnet
19. A. A. Belov, P. Behr, D. V. Vorontsov, B. V. Zubkov, A. A. Ilyin, S. K. Kalashnikov, A. P. Kalinin, S. Montenegro, A. M. Ovchinnikov, M. Yu. Ovchinnikov, A. G. Orlov, A. N. Ostanniy, S. Pletner, I. V. Ritus, A. I. Rodionov, I. D. Rodionov, I. P. Rodionova, “The software for the distributed on-board computer system prototype”, Keldysh Institute preprints, 2004, 014, 25 pp.  mathnet
2003
20. A. A. Ilyin, A. M. Ovchinnikov, M. Yu. Ovchinnikov, “Principles of operation and design of the active-pixel sensors”, Keldysh Institute preprints, 2003, 085, 25 pp.  mathnet
21. A. A. Ilyin, “Image processing for the testbed vehicle navigation”, Keldysh Institute preprints, 2003, 073, 24 pp.  mathnet
22. A. A. Belov, D. V. Vorontsov, A. A. Ilyin, M. Yu. Ovchinnikov, A. G. Orlov, A. A. Ponomarev, I. D. Rodionov, R. S. Salikhov, N. N. Khrenov, “The russian small satellite for hyperspectral monitoring of gas pipelines”, Keldysh Institute preprints, 2003, 012, 14 pp.  mathnet
2002
23. M. Yu. Ovchinnikov, V. I. Pen'kov, I. Yu. Kiryushkin, R. B. Nemuchinsky, A. A. Ilyin, E. E. Nokhrina, “Experience in the development, building and usage of a magnetic attitude control system for small satellites”, Keldysh Institute preprints, 2002, 053, 32 pp.  mathnet
2001
24. N. A. Zaitsev, A. A. Ilyin, Yu. B. Radvogin, “Analysis of the stationary viscous incompressible flow in a section of a pipe between two moving partitions”, Keldysh Institute preprints, 2001, 075  mathnet
25. A. A. Ilyin, S. P. Nepobedimyi, M. Yu. Ovchinnikov, A. I. Rodionov, I. B. Shilov, “Recognition of the objects using data of Microrelief 3D-Detector (MDM-locator)”, Keldysh Institute preprints, 2001, 072  mathnet
26. A. A. Ilyin, S. P. Nepobedimyi, M. Yu. Ovchinnikov, A. I. Rodionov, I. D. Rodionov, I. B. Shilov, “The mathematical processing methods of Microrelief 3D-Detector Data (MDM-locator)”, Keldysh Institute preprints, 2001, 071  mathnet
27. A. A. Ilyin, S. P. Nepobedimyi, A. I. Rodionov, I. D. Rodionov, I. B. Shilov, “Technical active 3D-vision system (MDM-locator)”, Keldysh Institute preprints, 2001, 062  mathnet
28. N. A. Zaitsev, A. A. Ilyin, Yu. B. Radvogin, “Analysis of the two-dimensional stationary viscous incompressible flow in a rectangular domain with moving walls”, Keldysh Institute preprints, 2001, 033, 31 pp.  mathnet
2000
29. A. A. Ilyin, V. V. Chepyzhov, “On the fractal dimension of invariant sets; applications to Navier-Stokes equations”, Keldysh Institute preprints, 2000, 022  mathnet
1998
30. O. A. Bukin, I. V. Bazarov, N. S. Bodin, A. A. Ilyin, V. D. Kiselev, È. A. Sviridenkov, V. I. Tsarev, A. Yu. Maior, “Influence of the pressure of a gaseous atmosphere on the characteristics of the emission spectra of a laser plasma generated on the surfaces of solid targets”, Kvantovaya Elektronika, 25:8 (1998),  705–708  mathnet [Quantum Electron., 28:8 (1998), 685–688  isi]
31. A. A. Ilyin, “Best constants in a class of polymultiplicative inequalities for derivatives”, Mat. Sb., 189:9 (1998),  61–84  mathnet  mathscinet  elib; Sb. Math., 189:9 (1998), 1335–1359  isi  scopus
1996
32. A. A. Ilyin, “Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides”, Mat. Sb., 187:5 (1996),  15–58  mathnet  mathscinet  zmath  elib; Sb. Math., 187:5 (1996), 635–677  isi  scopus
1993
33. A. A. Ilyin, “Partly dissipative semigroups generated by the Navier–Stokes system on two-dimensional manifolds, and their attractors”, Mat. Sb., 184:1 (1993),  55–88  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 78:1 (1994), 47–76  isi
1991
34. A. A. Ilyin, “The Euler equations with dissipation”, Mat. Sb., 182:12 (1991),  1729–1739  mathnet  mathscinet  zmath; Math. USSR-Sb., 74:2 (1993), 475–485  isi
1990
35. A. A. Ilyin, “The Navier–Stokes and Euler equations on two-dimensional closed manifolds”, Mat. Sb., 181:4 (1990),  521–539  mathnet  mathscinet  zmath; Math. USSR-Sb., 69:2 (1991), 559–579  isi
1989
36. A. A. Ilyin, A. N. Filatov, “Stability of stationary solutions of equations of a barotropic atmosphere with respect to linear approximation”, Dokl. Akad. Nauk SSSR, 306:6 (1989),  1362–1365  mathnet  mathscinet; Dokl. Math., 34:6 (1989), 516–518
1988
37. A. A. Ilyin, A. N. Filatov, “Unique solvability of the Navier–Stokes equations on a two-dimensional sphere”, Dokl. Akad. Nauk SSSR, 301:1 (1988),  18–22  mathnet  mathscinet  zmath; Dokl. Math., 38:1 (1989), 9–13

Presentations in Math-Net.Ru
1. Спектральные неравенства и гидродинамика на сфере
A. A. Ilyin
Differential equations, analysis and control: theory and applications
November 12, 2018 18:30
2. Спектральные неравенства на сфере
A. A. Ilyin
Differential equations, analysis and control: theory and applications
November 20, 2017 18:30
3. Магнитные интерполяционные неравенства и неравенства Карлсона-Ландау
A. A. Ilyin
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
April 15, 2015 16:00
4. Интерполяционные неравенства для разностных операторов и приложения к спектральной теории
A. A. Ilyin
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
October 15, 2014 16:00
5. Асимптотика функций Грина эллиптических операторов высокого порядка. Точные константы в неравенствах Гальярдо–Ниренберга для одного класса периодических функций
A. A. Ilyin
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
December 12, 2012 16:00
6. Применение экстремальных эллипсоидов в задачах представления данных при суррогатном моделировании
V. V. Chepyzhov, A. A. Ilyin
PreMoLab Seminar
October 4, 2012 17:00
7. Averaging and regularity of solutions of the periodic KdV equation
A. A. Ilyin
Sinai Seminar
June 26, 2012 14:00
8. О регулярности решений периодического уравнения Кортевега–де Фриза
A. A. Ilyin
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
October 21, 2009 16:00
9. Аттракторы уравнений Навье–Стокса
A. A. Ilyin
Seminar by Department of Differential Equation, Steklov Mathematical Institute of RAS
September 28, 2005

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