RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 
Cheban, David Nikolaevich

Statistics Math-Net.Ru
Total publications: 30
Scientific articles: 29

Number of views:
This page:1254
Abstract pages:3415
Full texts:1123
References:315
Professor
Doctor of physico-mathematical sciences (1991)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail: , ,
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:
  1. Cheban D. N., “Ogranichennye resheniya lineinykh pochti periodicheskikh sistem differentsialnykh uravnenii”, Izvestiya RAN. Seriya matematicheskaya, 62:3 (1998), 155–174  mathnet  mathscinet  zmath
  2. Cheban D. N., “Uniform exponential stability of linear almost periodic systems in Banach spaces”, Electronic Journal of Differential Equations, 2000, no. 29, 18 p.  mathscinet
  3. 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  mathscinet
  4. 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  crossref  mathscinet  zmath
  5. Cheban D. N., “Global pullback attractors of $\mathbb C$-analytic nonautonomous dynamical systems”, Stochastics and Dynamics, 1:4 (2001), 511–535  crossref  mathscinet  zmath

http://www.mathnet.ru/eng/person8878
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/196743

Publications in Math-Net.Ru
2015
1. 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, 2,  42–60  mathnet
2014
2. David Cheban, “Compact global attractors of non-autonomous gradient-like dynamical systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, 2,  85–101  mathnet
2013
3. David Cheban, “Asymptotic stability of infinite-dimensional nonautonomous dynamical systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2013, 1,  11–44  mathnet  mathscinet  zmath
2009
4. D. Cheban, C. Mammana, E. Michetti, “Global attractors of non-autonomous difference equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, 1,  45–57  mathnet  mathscinet  zmath
2008
5. D. Cheban, C. Mammana, E. Michetti, “Global Attractors of Quasi-Linear Non-Autonomous Difference Equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, 1,  84–104  mathnet  mathscinet  zmath
2005
6. D. Cheban, C. Mammana, “Absolute Asymptotic Stability of Discrete Linear Inclusions”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2005, 1,  43–68  mathnet  mathscinet  zmath
2004
7. D. Cheban, C. Mammana, “Asymptotic Stability of autonomous and Non-Autonomous Discrete Linear Inclusions”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, 3,  41–52  mathnet  mathscinet  zmath
2003
8. David N. Cheban, Peter E. Kloeden, Björn Schmalfuß, “Global attractors for $V$-monotone nonautonomous dynamical systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, 1,  47–57  mathnet  mathscinet  zmath
2000
9. 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  mathnet  mathscinet  zmath; Math. Notes, 68:6 (2000), 790–793  isi
1998
10. D. N. Cheban, “Bounded solutions of linear almost periodic differential equations”, Izv. RAN. Ser. Mat., 62:3 (1998),  155–174  mathnet  mathscinet  zmath; Izv. Math., 62:3 (1998), 581–600  isi  scopus
11. D. N. Cheban, “Asymptotics of solutions of infinite-dimensional homogeneous dynamical systems”, Mat. Zametki, 63:1 (1998),  115–126  mathnet  mathscinet  zmath; Math. Notes, 63:1 (1998), 102–111  isi
1995
12. 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  mathnet  mathscinet; Differ. Equ., 31:12 (1995), 1995–1998
13. 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  mathnet  mathscinet  zmath; Math. Notes, 57:1 (1995), 100–102  isi
1990
14. 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  mathnet  mathscinet  zmath
1989
15. D. N. Cheban, “Nonautonomous dynamical systems with convergence”, Differ. Uravn., 25:9 (1989),  1633–1635  mathnet  mathscinet  zmath
16. D. N. Cheban, “A problem of J. Hale”, Mat. Zametki, 46:1 (1989),  120–121  mathnet  mathscinet  zmath
17. D. N. Cheban, “Nonautonomous dissipative dynamical systems with a hyperbolic subset of the center (one-dimensional case)”, Mat. Zametki, 45:6 (1989),  93–98  mathnet  mathscinet  zmath; Math. Notes, 45:6 (1989), 495–498  isi
1988
18. D. N. Cheban, “On the structure of the Levinson center of a dissipative dynamical system”, Differ. Uravn., 24:9 (1988),  1564–1576  mathnet  mathscinet; Differ. Equ., 24:9 (1988), 1031–1040
1987
19. D. N. Cheban, “Nonautonomous dissipative dynamical systems. The method of Lyapunov functions”, Differ. Uravn., 23:3 (1987),  464–474  mathnet  mathscinet  zmath
1986
20. D. N. Cheban, “Nonautonomous dissipative dynamical systems”, Dokl. Akad. Nauk SSSR, 286:4 (1986),  824–827  mathnet  mathscinet  zmath
21. D. N. Cheban, “$C$-analytic dissipative dynamical systems”, Differ. Uravn., 22:11 (1986),  1915–1922  mathnet  mathscinet
22. D. N. Cheban, “Quasiperiodic solutions of dissipative systems with quasiperiodic coefficients”, Differ. Uravn., 22:2 (1986),  267–278  mathnet  mathscinet
1984
23. D. N. Cheban, “Stability of the Levinson center of nonautonomous dissipative dynamical systems”, Differ. Uravn., 20:11 (1984),  2016–2018  mathnet  mathscinet  zmath
24. D. N. Cheban, “Periodic and quasiperiodic solutions of linear differential equations”, Differ. Uravn., 20:8 (1984),  1455–1456  mathnet  mathscinet  zmath
1978
25. 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  mathnet  mathscinet  zmath
26. D. N. Cheban, “Some properties of the solutions of linear differential equations with asymptotically almost periodic coefficients”, Differ. Uravn., 14:5 (1978),  940–942  mathnet  mathscinet  zmath
1977
27. 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  mathnet  mathscinet  zmath
28. D. N. Cheban, “Solutions of operator equations that are asymptotically stable in the sense of Poisson”, Differ. Uravn., 13:8 (1977),  1411–1417  mathnet  mathscinet  zmath
29. 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  mathnet  mathscinet  zmath

1999
30. D. N. Cheban, “Letter to the editors”, Izv. RAN. Ser. Mat., 63:3 (1999),  224  mathnet  mathscinet

Organisations
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019