01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
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Keywords:
dynamical systems,
nonautonomous dynamical systems,
topological theory of dynamical systems,
global attractors,
almost periodical systems,
linear differential equations in the Banach spaces.
Subject:
I) Global attractors of nonautonomous dynamical systems. There was developed a general theory of compact global attractors of autonomous and nonautonomous dynamical systems. Different types of attractors were introduced, there is given a description of these classes of attractors and there are established relations between them. The structure of compact global attractor for different classes of systems (linear; homogeneous; C-analytic; the systems with a hyperbolic centre etc) was studied. There was developed the method of Lyapunov's functions for study of compact global attractors of nonautonomous dynamical systems. The conditions of existence of compact global atractors for certain classes of evolutionary equations (quasilinear systems; C-analytic systems; quasihomogeneous systems; monotone systems; systems of Lorenz; Navier–Stokes"s equations etc) are given. There was established an upper semicontinuos dependance of small parameter of compact global attractor.
II) Linear nonautonomous dynamical systems in Banach spaces. Different types of stabilities for linear differential equations with almost periodic coefficients and relations between them were studied. For the linear equations in Banach spaces the well-known theorem of Cameron–Johnson was generalized.
Biography
Graduated from Faculty of Mathematics and Cibernetics of State University of Moldova (SUM) in 1974 (department of differential equations). Ph.D. thesis was defended in 1978. D.Sci. thesis was defended in 1991. A list of my works contains about 100 titles, including three monographs.
Main publications:
Cheban D. N., “Ogranichennye resheniya lineinykh pochti periodicheskikh sistem differentsialnykh uravnenii”, Izvestiya RAN. Seriya matematicheskaya, 62:3 (1998), 155–174
Cheban D. N., “Uniform exponential stability of linear almost periodic systems in Banach spaces”, Electronic Journal of Differential Equations, 2000, no. 29, 18 p.
Cheban D. N., “Global attractors of nonautonomous quasihomogeneous dynamical systems”, Proceedings of the International Conference on Dynamical Systems and Differential Equations (May 18–21, 2000, Kennesaw, USA), Discrete Contin. Dynam. Systems, 2001, Added Volume, 96–101
Cheban D. N., Kloeden P. E., Schmalfuß B., “Pullback attractors in dissipative nonautonomous differential equations under discretization”, J. Dynam. Differential Equations, 13:1 (2001), 185–213
Cheban D. N., “Global pullback attractors of $\mathbb C$-analytic nonautonomous dynamical systems”, Stochastics and Dynamics, 1:4 (2001), 511–535
David Cheban, “Different types of compact global attractors for cocycles with a noncompact phase space of driving system and the relationship between them”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, no. 1, 35–55
David Cheban, “Almost periodic and almost automorphic solutions of monotone differential equations with a strict monotone first integral”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 3, 39–74
2019
5.
David Cheban, “Levitan almost periodic solutions of infinite-dimensional linear differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 2, 56–78
2015
6.
David Cheban, “Relation between Levinson center, chain recurrent set and center of Birkhoff for compact dissipative dynamical systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 2, 42–60
D. Cheban, C. Mammana, “Asymptotic Stability of autonomous and Non-Autonomous Discrete Linear Inclusions”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, no. 3, 41–52
David N. Cheban, Peter E. Kloeden, Björn Schmalfuß, “Global attractors for $V$-monotone nonautonomous dynamical systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, no. 1, 47–57
2000
14.
D. N. Cheban, “An Analog of the Cameron–Johnson Theorem for Linear $\mathbb C$-Analytic Equations in Hilbert Space”, Mat. Zametki, 68:6 (2000), 935–938; Math. Notes, 68:6 (2000), 790–793
1998
15.
D. N. Cheban, “Bounded solutions of linear almost periodic differential equations”, Izv. RAN. Ser. Mat., 62:3 (1998), 155–174; Izv. Math., 62:3 (1998), 581–600
D. N. Cheban, “On the structure of compact asymptotically stable invariant sets of $C$-analytic almost periodic systems”, Differ. Uravn., 31:12 (1995), 2025–2028; Differ. Equ., 31:12 (1995), 1995–1998
18.
D. N. Cheban, “Converse of Lyapunov's theorem on asymptotic stability to the first approximation for $C$-analytic nonautonomous systems”, Mat. Zametki, 57:1 (1995), 139–142; Math. Notes, 57:1 (1995), 100–102
D. N. Cheban, “On the structure of the Levinson center of a dissipative dynamical system with the hyperbolicity condition on the closure of the set of recurrent motions”, Differ. Uravn., 26:5 (1990), 913–914
1989
20.
D. N. Cheban, “Nonautonomous dynamical systems with convergence”, Differ. Uravn., 25:9 (1989), 1633–1635
21.
D. N. Cheban, “A problem of J. Hale”, Mat. Zametki, 46:1 (1989), 120–121
22.
D. N. Cheban, “Nonautonomous dissipative dynamical systems with a hyperbolic subset of the center (one-dimensional case)”, Mat. Zametki, 45:6 (1989), 93–98; Math. Notes, 45:6 (1989), 495–498
D. N. Cheban, “On the structure of the Levinson center of a dissipative dynamical system”, Differ. Uravn., 24:9 (1988), 1564–1576; Differ. Equ., 24:9 (1988), 1031–1040
D. N. Cheban, “Quasiperiodic solutions of dissipative systems with quasiperiodic coefficients”, Differ. Uravn., 22:2 (1986), 267–278
1984
28.
D. N. Cheban, “Stability of the Levinson center of nonautonomous dissipative dynamical systems”, Differ. Uravn., 20:11 (1984), 2016–2018
29.
D. N. Cheban, “Periodic and quasiperiodic solutions of linear differential equations”, Differ. Uravn., 20:8 (1984), 1455–1456
1978
30.
D. N. Cheban, V. F. Cherny, “On the question of an exponential dichotomy on the half-line of the solutions of linear systems of differential equations”, Differ. Uravn., 14:11 (1978), 2012–2018
31.
D. N. Cheban, “Some properties of the solutions of linear differential equations with asymptotically almost periodic coefficients”, Differ. Uravn., 14:5 (1978), 940–942
1977
32.
D. N. Cheban, “On the question of the structural stability of linear systems of differential equations with almost periodic coefficients”, Differ. Uravn., 13:11 (1977), 2099–2101
33.
D. N. Cheban, “Solutions of operator equations that are asymptotically stable in the sense of Poisson”, Differ. Uravn., 13:8 (1977), 1411–1417
B. A. Shcherbakov, D. N. Cheban, “Asymptotically Poisson stable motions of dynamical systems, and their comparability with regard to the recurrence property in the limit”, Differ. Uravn., 13:5 (1977), 898–906
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