01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
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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.
A. G. Kostyanko, D. Stone, A. A. Ilyin, S. V. Zelik, “Multi-vortices and lower bounds for the attractor dimension of 2D Navier–Stokes equations”, Dokl. RAN. Math. Inf. Proc. Upr., 516 (2024), 98–102; Dokl. Math., 109:2 (2024), 179–182
2023
2.
S. V. Zelik, A. A. Ilyin, “On a class of interpolation inequalities on the 2D sphere”, Mat. Sb., 214:3 (2023), 120–134; Sb. Math., 214:3 (2023), 396–410
2022
3.
S. V. Zelik, A. A. Ilyin, A. G. Kostyanko, “Estimates for the Dimension of Attractors of a Regularized Euler System with Dissipation on the Sphere”, Mat. Zametki, 111:1 (2022), 54–66; Math. Notes, 111:1 (2022), 47–57
S. V. Zelik, A. A. Ilyin, A. G. Kostyanko, “Sharp dimension estimates for the attractors of the regularized damped Euler system”, Dokl. RAN. Math. Inf. Proc. Upr., 499 (2021), 13–16; Dokl. Math., 104:1 (2021), 169–172
A. A. Ilyin, A. A. Laptev, “Magnetic Lieb–Thirring inequality for periodic functions”, Uspekhi Mat. Nauk, 75:4(454) (2020), 207–208; Russian Math. Surveys, 75:4 (2020), 779–781
S. V. Zelik, A. A. Ilyin, A. A. Laptev, “On the Lieb–Thirring Constant on the Torus”, Mat. Zametki, 106:6 (2019), 946–950; Math. Notes, 106:6 (2019), 1020–1024
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; Math. Notes, 101:4 (2017), 746–750
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.
S. V. Zelik, A. A. Ilyin, “Green's function asymptotics and sharp interpolation inequalities”, Uspekhi Mat. Nauk, 69:2(416) (2014), 23–76; Russian Math. Surveys, 69:2 (2014), 209–260
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; Sb. Math., 205:2 (2014), 220–223
A. A. Ilyin, “Lower bounds for sums of eigenvalues of elliptic operators and systems”, Mat. Sb., 204:4 (2013), 103–126; Sb. Math., 204:4 (2013), 563–587
2012
14.
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.
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.
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.
A. A. Ilyin, “Lieb–Thirring Integral Inequalities and Sharp Bounds for the Dimension of the Attractor of the Navier–Stokes Equations with Friction”, Trudy Mat. Inst. Steklova, 255 (2006), 146–160; Proc. Steklov Inst. Math., 255 (2006), 136–149
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.
A. A. Ilyin, “Lieb–Thirring integral inequalities and their applications to attractors of the Navier–Stokes equations”, Mat. Sb., 196:1 (2005), 33–66; Sb. Math., 196:1 (2005), 29–61
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.
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.
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.
2003
24.
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.
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.
2002
27.
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.
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
29.
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
30.
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
31.
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
32.
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.
2000
33.
A. A. Ilyin, V. V. Chepyzhov, “On the fractal dimension of invariant sets; applications to Navier-Stokes equations”, Keldysh Institute preprints, 2000, 022
1998
34.
A. A. Ilyin, “Best constants in a class of polymultiplicative inequalities for derivatives”, Mat. Sb., 189:9 (1998), 61–84; Sb. Math., 189:9 (1998), 1335–1359
A. A. Ilyin, “Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides”, Mat. Sb., 187:5 (1996), 15–58; Sb. Math., 187:5 (1996), 635–677
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; Russian Acad. Sci. Sb. Math., 78:1 (1994), 47–76
A. A. Ilyin, “The Navier–Stokes and Euler equations on two-dimensional closed manifolds”, Mat. Sb., 181:4 (1990), 521–539; Math. USSR-Sb., 69:2 (1991), 559–579
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; Dokl. Math., 34:6 (1989), 516–518
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; Dokl. Math., 38:1 (1989), 9–13
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