english title
 
Igor Chueshov
Doctor of Physical and Mathematical Sciences, Professor of Mathematics
Head of Department
E-mail  chueshov@karazin.ua
Date of Birth  September 23, 1951
Place of Birth  Leningrad, Russia
Education  

School of Mechanics and Mathematics of Kharkov State University (1968-1973)

Post-Graduate Education  

 School of Mechanics and Mathematics of Kharkov State University (1974-1977). Scientific supervisor: Professor V.A.Scherbina. Candidate (PhD) dissertation (1977) studied some dynamical problems arising in Quantum Theory. Doctorate dissertation (1990) was devoted to a mathematical description of a nonregular long-time behavior of infinite dimensional dynamical systems arising in Nonlinear Oscillations Theory. The official opponents on the doctorate dissertation: Prof. M. I. Vishik, Prof. N. F. Morozov, Prof. E. Ya. Khruslov.

Profesional Positions  

Assistant Professor ( 1973-1974, 1977-1980), Associate Professor (1980-1991), Professor (1991-present) of the School of Mechanics and Mathematics, Head (2000-present) of the Department of Mathematical Physics and Computational Mathematics at V. Karazin Kharkov National University.  Reviewer of "Mathematical Reviews" (1993 - present). The Corresponding Member of National Academy of Science of Ukraine (since February 2009).

Associate editor  in the following journals:

 

  •  "Journal of Mathematical Physics, Analysis, Geometry" (1993-present),
  • "Stochastics and Dynamics" (2000-present),
  • "Ukrainian Mathematical Journal" (2008 - present)
  • "International Journal of Differential Equations" (2009 - present).  
  • Evolution Equations and Control Theory (2012 - present),
    "Nonlinear Analysis, Real World Applications" (2012 - present)
  • "Discrete and Continuous Dynamical Systems - Series B" (2012 - present). 
  • "Evolution Equations and Control Theory" (2012-present).  
Research Interests  

The most part of my research deals with a nonregular and long-time behavior of infinite dimensional dissipative dynamical systems arising in Mechanics and Physics. I investigated both deterministic and stochastic dynamical systems generated by nonlinear partial differential equations (PDE). In particular, well-posedness and the existence of finite-dimensional attractors were proved for evolution von Karman equations and for certain their modifications; the continuity properties of these attractors are studied; the theory of inertial and approximate inertial manifolds was developed for wide classes of deterministic and stochastic systems. The main applications of these investigations was the nonlinear flutter problem in air-space systems and turbulence phenomena in certain systems described by semilinear parabolic PDE. I have also the papers on mathematical problems of Quantum Theory. The total number of the published scientific articles is more than 100. I have published the 3 research monograph: (i) "Monotone Random Systems", LMN1779, Springer, 2002; (ii) (jointly with I.Lasiecka) "Long-time behaviour of second order evolution equations with nonlinear damping", Mem.AMS, no.912, Amer.Math.Soc., Providence, RI, 2008; (iii) (jointly with I.Lasiecka) Von Karman evolution equations, Springer, New-York, 2010. 

 (jointly with I.Lasiecka) Von Karman evolution equations, Springer,
New-York, 2010.  (jointly with I.Lasiecka) Von Karman evolution equations, Springer,New-York, 2010. 
Participation in Confernces  

The main results of my research were presented on the following conferences:


1. VI and VII All-Union Conferences "Complex Analysis and Differential Equations", Chernogolovka, Russia, March, 1987, 1989.


2. XI, XV and XIX Annual Meetings of Petrovsky Seminar and Moscow Mathematical Society, Moscow, Russia, January, 1988, 1993, 1998.


3. International Conference "Dynamical Systems and Turbulence", Katsiveli, Crimea, Ukraine, May, 1991.


4. Third International Conference "Evolutionary Stochastic Systems in Physics and Biology", Katsiveli, Crimea, Ukraine, May, 1992.


5. International Conference "Lyapunov Readings", Kharkov, Ukraine, September, 1992.


6. First European Nonlinear Oscillations Conference, Hamburg, Germany, Aug., 1993.


7. Szecho-Slovak Conference on Differential Equations and Their Applications (EQUADIFF8), Bratislava, Slovakia, August, 1993.


8. International Conference "Differential Equations: Bifurcations and Chaos", Katsiveli, Crimea, Ukraine, May, 1994.


9. CIRM Conference "Stochastic Partial Differential Equations and Random Media", Marsseille, France, May-June, 1994.


10. The Third International Congress on Industrial and Applied Mathematics, Hamburg, Germany, July, 1995.


11. VII and VIII International Conference "Nonlinear Differential Equations", Kiev, Ukraine, August, 1995, 1997, 2001.


12. International Conference "Differential Equations and Related Topics", Moscow, Russia, April, 1996; May, 2001; May 2011.


13. The Third Scandinavian-Ukrainian Conference in Probability and Statistics, Kiev, Ukraine, June, 1999.


14. International Conference on Differential Equations EDUADIFF99, Berlin, Germany, August, 1999.


15. 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulations, Lausanne, Switzerland, August, 2000.

16. The Oberwolfach Research Institute meetings (see www.mfo.de): "Stochastic Evolution Equations and Applications" (Oct.2001) and "Dynamics and Applications of Stochastic Partial Differential Equation" (March 2002, organizer)

17. International conference "Analysis and Optimization of Differential Equations", Constanta, Romania, September, 2002.

18. International Conference on Differential Equations EDUADIFF-2003, Hasselt, Belgium, July, 2003. 


19. International Workshop on the Foundations of Nonautonomous Dynamical Systems, Friedrichsdorf am Taunus Germany,  September/October, 2003.

20.  AMS-IMS-SIAM Summer Research Conference "Control Methods in PDE - Dynamical Systems", Snowbird, Utah, USA, July, 2005.


21. International Conference on  Non-autonomous and Stochastic Dynamical Systems, Sevilla, Spain,  September/October, 2005.

22. International Congress "Nonlinear Dynamical Analysis - 2007", Saint-Petersburg, Russia, June 2007.

23. International Conference "Stochastic Analysis and Random Dynamical Systems", Lviv, Ukraine, June, 2009.

Differential and Functional 
Moscow, Russia, Aug

24. Sixth International Conference on Differential and Functional Differential Equations, Moscow, Russia, August 14-21, 2011.

25. International Conference in honor of Vladimir A. Marchenko's 90th birthday, Kharkov, Ukraine, August, 2012.

26. International Conference "Modern Stochastics: Theory and Applications, III"  Kiev, Ukraine, September, 2012.  

27.  Bogolyubov readings DIF-2013, Sevastopol, June 2013. 

Teaching Experience  

I have been giving within 5 last years the following courses: Equations of Mathematical Physics, Partial Differential Equations (PDE), Numerical Analysis, Operator Theory in Hilbert Spaces (for junior students); Attractors of Infinite-Dimensional Dynamical Systems, Inertial and Approximate Inertial Manifolds for Dissipative PDE Systems, Stochastic PDE and Their Applications, Evolution von Karman Equations (for senior and graduate students). I am the Head of the seminar in Long-Time Behavior of Nonlinear Dissipative PDE Systems. I have published by Kharkov University the following Courses of Lectures for senior and graduate students: Operator Methods in Mathematical Physics (1980); Waves in One-Dimensional Systems - Introduction (1991); The Mathematical Foundations of Nonregular Oscillation Theory of Infinite-Dimensional Systems (1991); Introduction to the Theory of Inertial Manifolds (1992). I have also published the books "Introduction to the Theory of Infinite-Dimensional Dissipative Systems", Acta, Kharkov, 1999, in Russian (English translation: Acta, Kharkov, 2002), "Random Monotone Systems. Theory and Applications", Springer, 2002.

Supervision of Theses  

I have supervised the thesis researches of senior students. These theses have been concerned with infinite dimensional dynamical systems.

I have successfully supervised the PhD theses:

  • A.V.Rezounenko, "Long-Time Behaviour of Solutions to a Class of   Retarded Partial Differential Equations", 1997.
  • A.M.Rekalo, "Qualitative Behaviour of Solutions of Nonlinear Parabolic  Equations in Thin Two-Layer Domains", 2004.
  • A.S.Shcherbina, "Asymptotic Behaviour of Solutions of the Dissipative  Zakharov System", 2006.
  • T.B.Fastovska, "Asymptotic Behaviour  of Solutions to the  Mindlin Plates Thermoelastic Problems", 2007.
  • I.A.Ryzhkova, "Asymptotic Dynamics of a Thermoelastic von   Karman Plate in a Gas Flow", 2008.
  • O.A. Naboka, "Synchronization in the Dynamical Problems of Nonlinear Infinite Dimensional Coupled Systems", 2010.
  • M.Yu. Potomkin, "Asymptotic Dynamics of Nonlinear Elastic Plates with Memory", 2011.
Publications  

BOOKS:

Chueshov I. and  Lasiecka I. (2010), Von Karman  Evolution Equations, Springer, New York, 2010, 778 p.; http://www.springerlink.com/content/978-0-387-87711-2

Chueshov I. and Lasiecka I. (2008), Long-time Behaviour of Second Order Evolution Equations with Nonlinear Damping, Memoirs of AMS no 912, Amer.Math.Soc., Providence, RI. http://www.ams.org/bookstore-getitem/item=MEMO-195-912


Chueshov I. D. (2002) Monotone Random Systems. Theory and Application, (Lecture Notes in Mathematics, 1779). Springer, Berlin-Heidelberg-New York. http://www.springer.com/mathematics/probability/book/978-3-540-43246-3

Chueshov I.D. (1999) Introduction to the Theory of Infinite-Dimensional Dissipative Systems. Acta, Kharkov (Russian); English transl.: Acta, Kharkov, 2002; see also http://www.emis.de/monographs/Chueshov/ 

Chueshov I.D.(2014) Dynamics of Quasi-Stable Dissipative Systems, book in preparation, draft version  #4 of August 2014

 

BOOKS DETAILS


PAPERS:

2014: 

 Chueshov I., Dynamics of a nonlinear elastic plate interacting with a linearized compressible viscous fluid, Nonlinear Analysis, TMA 95,  650--665.

Chueshov I., Lasiecka I., and Webster J., Flow-plate interactions:  well-posedness and long-time behavior, Discrete Continuous Dynamical Systems Ser.S, 7,  925--965. 

Chueshov I., Lasiecka I., and Webster J., Attractors for delayed, nonrotational von Karman plates with applications to flow-structure interactions without any damping, Communications in Partial Differential Equations, 39, 1965--1997.

Chueshov I., A squeezing property and its applications to a description of long-time behaviour in the three-dimensional viscous primitive equations, Proceedings of the Royal Society of Edinburgh, 144A, 711--729.

2013: 

Chueshov I., Quantum Zakharov model in a bounded domain, Zeitschrift  Angewandte Mathematik  Physik 64,  967--989.

Chueshov I., Lasiecka I., Well-posedness and long time behavior in nonlinear dissipative hyperbolic-like evolutions with critical exponents, In: Nonlinear Hyperbolic PDEs, Dispersive and Transport Equations (HCDTE Lecture Notes, Part I), AIMS on Applied Mathematics Vol.6, G. Alberti  et al. (Eds.) AIMS,  Springfield, 2013, pp. 1--96.

Chueshov I. and Scheutzow M., Invariance and monotonicity  for stochastic delay differential equations, Discrete and Continuous  Dynamical Systems - B, 18, 1533--1554.

Chueshov I. and Ryzhkova I., 

Well-posedness and long time behavior 

for a class of fluid-plate interaction models, 

in: IFIP Advances in Information and Communication Technology, vol.391, 

25th IFIP TC7 Conference, 

Berlin, Sept.2011, D. H"omberg and F. Tr"oltzsch (Eds.), Springer, Berlin, 2013, pp.328--337. 

 
Chueshov I., Lasiecka I., and Webster J., Evolution semigroups in supersonic flow-plate interactions. J. Differential Equations, 254, 1741--1773.

Chueshov  I. and  Ryzhkova I., Unsteady interaction of a viscous fluid with an elastic shell modeled by full von Karman equations. J.  Differential Equations, 254, 1833-1862.

Chueshov  I. and  Ryzhkova I., A global attractor for a fluid-plate interaction model. Commun. Pure  Applied Analysis, 12,  1635--1656.

Chueshov  I. and  Ryzhkova I. On the interaction of an elastic wall with a Poiseuille-type flow, Ukrainian Mathematical Journal Volume 65, Issue 1,  158--177.

2012:

Chueshov I., Convergence of solutions of von Karman evolution equations to equilibria, Applicable Analysis, 91, 1699--1715.

Chueshov I.  and Shcherbina A., Semi-weak well-posedness and attractors for 2D Schroedinger-Boussinesq equtions, Evolution equations and Control Theory, v.1, 57--80. 

Chueshov I. and Lasiecka I., Generation of a semigroup and hidden regularity in nonlinear subsonic flow-structure interactions with absorbing boundary conditions, J. Abstract Diff. Equations and Appl., 3, 1--27. 

Chueshov I., Long-time dynamics of Kirchhoff wave models with strong nonlinear  damping, J. Differential Equations, 252,  1229--1262.

Chueshov I. and  Kolbasin S., Long-time dynamics in plate models with strong nonlinear  damping, Communications on  Pure and Applied Analysis, 11,  659--674.  

2011:

Chueshov I., A global attractor for a fluid–plate interaction  model accounting only for longitudinal deformations of the plate, Math. Meth. Appl. Sci., 34, 1801--1812.

Chueshov I. and  Millet A., Stochastic Two-Dimensional Hydrodynamical Systems: Wong-Zakai Approximation and Support Theorem. Stochastic Analysis and Applications,  29, no.4, 570--611. 

Chueshov I. and  Lasiecka I.,  On Global attractor  for  2D Kirchhoff-Boussinesq  model with  supercritical nonlinearity, Commun. in Partial Differential Equations, 36, no.1, 67--99.

2010

Chueshov I., Monotone Random Dynamical Systems in the Study of Biomathematical Models, Int. J. Biomathematics and Biostatistics, 1, no.2, 169-179.

 Chueshov I. and  Schmalfuss B., Master-slave synchronization and invariant manifolds  for coupled  stochastic systems, J. Math. Physics, 51, 102702.

Global attractors for a class of  Kirchhoff wave models 
with a structural  nonlinear  damping,
J. Abstract Diff. Equations and Applications,
1, no.1,  86--106. 

Chueshov I. , Global attractors for a class of  Kirchhoff wave models with a structural  nonlinear  damping, J. Abstract Diff. Equations and Applications, 1, no.1,  86--106. 

Chueshov I. and  Millet A., Stochastic 2D hydrodynamical type systems:  Well posedness and large deviations,  Appl. Math. Optim. 61, no.2,  379--420.

Chueshov I. and Kolbasin S., Plate models with state-dependent damping coefficient and their quasi-static limits, Nonlinear Analysis, 73, 1626--1644.

2009:

Chueshov I.,  Lasiecka I., and D.Toundykov D., Global Attractor for a Wave Equation with Nonlinear Localized Boundary Damping and a Source Term of Critical Exponent, J. Dynamics and Differential Equations, 21, no.2, 269-314.

2008

Chueshov I., Lasiecka I., and Toundykov D. Long-term dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent,Discrete and Continuous Dynamical Systems 20, no.3, 459--509.

Caraballo T., Real J., and  Chueshov I. Pullback attractors for stochastic heat equations in materials with  memory, Discrete and Continuous Dynamical Systems, Series B, 9, no.3-4, 525--539.

Chueshov I. and   Kuksin S. Random kick-forced 3D Navier-Stokes equations in a thin domain, Archive for Rational Mechanics and Analysis,  188, 117--153.

Chueshov I. and   Kuksin S.Stochastic 3D Navier-Stokes equations in a thin domain and its alpha-approximation, Physica D: Nonlinear Phenomena, 237, no.10-12, 1352--1367.

Chueshov I. Global unique solvability of 3D MHD equations in a thin periodic domain, Journal of Mathematical Analysis and Applications, 347, 224--234.

Bucci F. and   Chueshov I. Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations, Discrete and Continuous Dynamical Systems 22, no.3, 557--586.

Chueshov I. and Lasiecka I.  Long-time behaviour of second order evolution equations with nonlinear damping, Memoirs of AMS no 912, Amer.Math.Soc., Providence, RI.

Chueshov I. and Lasiecka I.  Attractors and long time behavior of von Karman thermoelastic plates,  Applied Mathematics and Optimization, 58, no.2, 195--241.

2007

Chueshov I.,  and  Lasiecka I. Long-time dynamics of  von Karman semi-flows with  nonlinear boundary/interior damping, J. Differential Equations,  233,  42--86.

Bucci F.,  Chueshov I.,  and  Lasiecka I. Global attractor for a composite system of nonlinear wave and plate equations, Communications on  Pure and Applied Analysis 6, 113--140.

Caraballo T., Chueshov I., Marin-Rubio P., and Real J. Existence and asymptotic behaviour for stochastic heat equations with multiplicative noise in materials with memory, Discrete and Continuous Dynamical Systems 18, no.2&3, 253--270.

Chueshov I. and Schmalfuss B. Qualitative behavior of a class of stochastic parabolic PDEs with dynamical boundary conditions, Discrete and Continuous Dynamical Systems 18, no.2&3,  315--338.

Caraballo T., Chueshov I., and  Kloeden P. Synchronization of a stochastic reaction-diffusion system on a thin two-layer domain, SIAM J. Math. Anal. 38, no.5, 1489--1507.

Chueshov I. and Lasiecka I.  Long-time dynamics of semilinear wave equation with nonlinear interior-boundary damping and sources of critical exponents,  in "Control Methods in PDE-Dynamical Systems", Contemp. Math., vol. 426, AMS, Providence, RI, 2007, 153--192.

Chueshov I.  Invariant manifolds and nonlinear master-slave synchronization in coupled systems, Applicable Analysis 86, no.3, 269--286.

Chueshov I. and Lasiecka I. Long time dynamics of von Karman evolutions with thermal effects, Boletim da Sociedade Paranaense de Matematica (3s) 25, 37--54.

2006

Chueshov I. and Lasiecka I. Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models, Discrete and Continuous Dynamical Systems 15, no. 3, 777–809.

Chueshov I.,  and  Lasiecka I. Global attractors for Mindlin--Timoshenko plates and  for their Kirchhoff limits, Milan Journal of Mathematics, 74, 117--138.

2005

Chueshov I., Shcherbina A. On 2D Zakharov system in a bounded domain. Differential and Integral Equations, 18, no. 7, 781–812.

Chueshov I. and Lasiecka I. Kolmogorov's epsilon-entropy for a class of invariant sets and dimension of global attractors for second order in time evolution equations with nonlinear damping, In: Control Theory of Partial Differential Equations, O.Imanuvilov et al. (eds). A Series of Lectures in Pure and Applied Mathematics, vol. 242, Chapman & Hall/CRC, Boca Raton, 2005, 51–69.

Chueshov I. and Siegmund S. On dimension and metric properties of trajectory attractors, Journal of Dynamics and Differential Equations, 17, no. 4, 621–641.

Chueshov I. and Schmalfuss B. Averaging of attractors and inertial manifolds for parabolic PDE with random coefficients, Advanced Nonlinear Studies 5, 461–492.

Chueshov I., Scheutzow M., Schmalfuss B. Continuity properties of inertial manifolds for stochastic retarded semilinear parabolic equations. In: Interacting Stochastic Systems, J-D. Deuschel, A. Greven (eds), Springer, Berlin—Heidelberg—New York, 353–375.

Arnold L., Chueshov I., Ochs G. Random dynamical systems methods in ship stability: a case study. In: Interacting Stochastic Systems, J-D. Deuschel, A. Greven (eds), Springer, Berlin—Heidelberg—New York, 409–433.

Chueshov I., Raugel G., Rekalo A. Interface boundary value problem for the Navier-Stokes equations in thin two-layer. J. Diff. Equations, 208, 449–493.

Caraballo T., Chueshov I., Langa J. Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations. Nonlinearity, 18, 747–767.

2004

I. Chueshov and I. Lasiecka, Global attractors for von Karman evolutions with a nonlinear boundary dissipation, J. Diff. Equations 198 (2004), 196-231.

I. D. Chueshov, A. M. Rekalo, Global attractor of contact parabolic problem on thin two-layer domain, Matem. Sbornik v. 195 (2004), no. 1, 103-128, in Russian; English translation in Sbornik: Mathematics v. 195 (2004), no. 1.

Chueshov I., Lasiecka I. Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping. Preprint SNS, no. 14 (http://math.sns.it/papers/chulas04/)

Chueshov I. D., Eller M., Lasiecka I. Attractor and their structure for semilinear wave equations with nonlinear boundary dissipation. Bol. Soc. Paran. Mat., ser. 3, 22, no. 1, 38–57.

Chueshov I. D., Eller M., Lasiecka I. Finite dimensionality of the attractor for a semilinear wave equation with nonlinear boundary dissipation. Communications in Partial Differential Equations, 29, no. 11&12, 1847–1976.

Chueshov I., Schmalfuss B. Parabolic stochastic partial differential equations with dynamical boundary conditions, Differential and Integral Equations, 17, no. 7–8, 751–780.

Chueshov I., Polat M., Siegmund S. Gevrey regularity of global attractors for generalized Benjamin—Bona—Mahony equation. Matem. Fizika, Analiz, Geometriya, 11, no. 2, 226–242.

Chueshov I., Scheutzow M. On the structure of attractors and invariant measures for a class of monotone random systems. Dynamical Systems, 19, no. 2, 127–144.

Arnold L., Chueshov I., Ochs G. Stability and capsizing of ships in random sea — a survey. Nonlinear Dynamics 36, 135–179.

Chueshov I. D., Vuillermot P.-A. Non-random invariant sets for some systems of parabolic stochastic partial differential equations. Stoch. Anal. Appl. 22(6), 1421–1486.

Chueshov I. D. A reduction principle for coupled nonlinear parabolic-hyperbolic PDE. Journal of Evolution Equations 4, 591–612.

2003

Chueshov I., Lasiecka I. (2003) Determining functionals for a class of second order in time evolution equations with applications to von Karman equations, In: Analysis and Optimization of Differential Systems, V.Barbu et al. (eds), Kluwer, Boston-Dordrecht-London, 2003, 109-122.

Chueshov I., Duan J., Schmalfuss (2003) B. Determining functionals for random partial differential equations. Nonlin. Diff. Equations and Appl. 10, p.431-454.

L. Arnold, I. Chueshov, G. Ochs. Stability and capsizing of ships in random sea. Report # 464, Institut fuer Dynamische Systeme, Universitaet Bremen. (2003)

2002

Chueshov I. D. (2002) Monotone random systems. Theory and Application, (Lecture Notes in Mathematics, 1779). Springer, Berlin—Heidelberg—New York.

Chueshov I.D., Lasiecka I. (2002) Inertial manifolds for von Karman plate equations. Applied Math. Optim., 46, 179–206.

Chueshov I. D., Eller M., Lasiecka I. (2002) On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation. Communications in Partial Differential Equations, 27, no. 9&10, 1901-1951.

2001

Arnold L., Chueshov I. D. (2001) Cooperative random and stochastic differential equations. Discrete and Continuous Dyn. Systems, 7(1), 1-33.

Arnold L., Chueshov I. D. (2001) A limit set trichotomy for order-preserving random systems. Positivity 5(2), 95-114.

Berge B., Chueshov I. D., Vuillermot P. -A. (2001) On behavior of solutions to certain parabolic SPDE's driven by Wiener processes. Stoch. Processes Appl. 92, 237-263.

Chueshov I. D., Scheutzow M. (2001) Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations. J. of Dyn. and Diff. Eqs., 13, no. 2, 355-380.

Chueshov I. D., Kalantarov V. K. (2001) Determining functionals for nonlinear damped wave equations. Matem. Fizika, Analiz, Geometriya, 5, no. 2, 215-227.

Chueshov I. D. (2001) Order-preserving skew-product flows and nonautonomous parabolic systems. Acta Appl. Math., 65, 185-205.

Chueshov I. D., Duan J., Schmalfuss B. (2001) Probabilistic dynamics of two-layer geophysical flow. Stochastics and Dynamics, 1, 451-475.

2000

Chueshov I. D., Vuillermot P. -A. (2000) Long-time behavior of solutions to a class of stochastic parabolic equations with white noise: Ito's case. Stoch. Anal. Appl. 18(4), 581-615.

Chueshov I. D. (2000) Gevrey regularity of random attractors for stochastic reaction-diffusion equations. Random Operators and Stoch. Equations, 8(2), 143-162.

Bernier-Kazantsev C., Chueshov I. D. (2000) The finiteness of determining degrees of freedom for the quasi-geostrophic multi-layer ocean model. Nonlinear Analysis, 42, 1499-1512.

Chueshov I.D. (2000) Analyticity of global attractors and determining nodes for a class of damped nonlinear wave equations. Matematicheskij Sbornik, 191(10), 119-136 (Russian); English translation in Sbornik: Mathematics 191:2.

1999

Boutet de Monvel L., Chueshov I. D. (1999) On the oscillations of a von Karman plate in a potential gas flow. Izvestiya Russian Acad. Sci., 63, no.2, 3-28 (Russian); English translation in Izvestiya: Mathematics 63:2.

Chueshov I. D., Pankratov L. S. (1999), Upper semicontinuity of attractors of semilinear parabolic equations with asymptotically degenerating coefficients, Mat. Fiz., Analiz, Geom., 6, no. 1/2, 158-181.

Boutet de Monvel A., Chueshov I. D. (1999) The problem on interaction of von Karman plate with subsonic flow of gas. Math. Methods in the Appl. Sci., 22, 801-810.

Berge B., Chueshov I. D., Vuillermot P. -A. (1999) Lyapunov exponents for nonlinear SPDE's driven by finite-dimensional Wiener processes. C. R. Acad. Sci. Paris, ser. I, 329, 215-220.

Bourgeat A., Chueshov I. D., Pankratov L.S. (1999) Homogenization of attractors of semilinear parabolic equations in domains with spherical traps. C. R. Acad. Sci. Paris, ser. I. 329, 581-587.

Pankratov L. S., Chueshov I. D. (1999) Homogenization of attractors of non-linear hyperbolic equations with asymptotically degenerating coefficients. Matem. Sbornik, 190, no. 9, 99-126.

Chueshov I. D. (1999) On determining functionals for stochastic Navier-Stokes Equations. Stochastics and Stochastics Reports, 68, 45-64.

1998

Chueshov I. D., Vuillermot P. -A. (1998) Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients. Ann. Inst. Henri Poincare, Analyse non lineaire, 15, no. 2, 191-232.

Chueshov I. D., Vuillermot P. -A. (1998) Long-time behavior of solutions to a class of stochastic parabolic equations with white noise: Stratonovitch's case. Probability Theory and Related Fields, 112 (2), 149-202.

Chueshov I. D., Vuillermot P. -A. (1998) On the large-time dynamics of a class of parabolic equations subjected to homogeneous white noise: Ito's case. C. R. Acad. Sci. Paris, ser.I, 326, 1299-1304.

Boutet de Monvel A., Chueshov I. D. (1998) Uniqueness theorem for weak solutions of von Karman evolution equations. J. of Math. Anal. and Appl., 221, 419-429.

Arnold L., Chueshov I. D. (1998) Order-preserving random dynamical systems: equilibria, attractors, applications. Dynamics and Stability of Systems, 13, 265-280.

Boutet de Monvel L., Chueshov I. D., Rezounenko A. V. (1998) Inertial manifolds for retarded semilinear parabolic equations, Nonlinear Analysis, 34, 907-925.

Chueshov I. D. (1998) Remark on sets of determining elements for reaction-diffusion systems. Math. Notes, 63, no.5, 774-784.

Chueshov I. D. (1998) Theory of functionals that uniquely determine asymptotic dynamics of infinite-dimensional dissipative systems. Uspekhi Matem. Nauk, 53, no. 4, 77-124 (Russian); English translation in Russian Math. Surveys 53:4.

Chueshov I. D. (1998) Boundary determining functionals for dissipative initial boundary value problems. Uspekhi Matem. Nauk, 53, no. 4, 174-175 (Russian).

Chueshov I. D. (1998) On functionals that completely determine long-time behaviour of dissipative systems. Nonlinear Boundary-Values Problems, 6. c.70-80.

1997

Chueshov I. D. (1997) On the finiteness of the number of determining elements for von Karman evolution equations. Math. Meth. in the Appl. Sci. 20, no. 10, 855-865.

Boutet de Monvel L., Chueshov I. D., Rezounenko A. V. (1997) Long-time behaviour of strong solutions of retarded nonlinear PDE's. Communications in Partial Differential Equations, 22, no. 9 and 10, 1453-1474.

Boutet de Monvel L., Chueshov I. D., Khruslov E. Ya. (1997) Homogenization of attractors for semilinear parabolic equations on manifolds with complicated microstructure. Annali di Matematica pura ed applicata, 172, 297-322.

Chueshov I. D. (1997) On asymptotically determining functionals for dissipative systems. Institut fur Dynamische Systeme, Universitat Bremen. Report 414, 19 p.

1996

Chueshov I. D. (1996) On a construction of approximate inertial manifolds for second order in time evolution equations. Nonlinear Analysis, TMA, 26, no. 5, 1007-1021.

Boutet de Monvel L., Chueshov I. D. (1996) Non-linear oscillations of a plate in a flow of gas. C. R. Acad. Sci. Paris, ser. I, 322, 1001-1006.

Chueshov I. D., Vuillermot P. -A. (1996) On the large-time dynamics of a class of random parabolic equations. C. R. Acad. Sci. Paris, ser.I, 322, 1181-1186.

Chueshov I. D., Vuillermot P. -A. (1996) On the large-time dynamics of a class of parabolic equations subjected to homogeneous white noise: Stratonovitch's case. C. R. Acad. Sci. Paris, ser.I, 323, 29-33.

Chueshov I. D. (1996) On a description of long-time behaviour of dissipative perturbations of infinite dimensional Hamiltonian systems. Z. angew. Math. Mech., 76, s.2, 53-56.

1995

Chueshov I. D. (1995) Correct solvability, attractors and statistical solutions for problem of nonlinear oscillations of elastic shallow shell in flow of gas. - In: Evolutionary stochastic systems in Physics and Biology, V. S. Korolyuk et al. (eds.), Proc. III Intern. Conf., Katsiveli, May 3-14, 1992, TVP Sci. Publ, 1995, 250-256.

Chueshov I. D., Girya T. V. (1995) Inertial manifolds and forms for semilinear parabolic equations subjected to additive white noise. Letters in Math. Physics, 34, no. 1, 69-76.

Chueshov I. D., Girya T. V. (1995) Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems. Matem. Sbornik, 186, no. 1, 29-46 (Russian); English transl. in Sbornik: Mathematics, 186, no. 1 (1995).

Chueshov I. D. (1995) On approximate inertial manifolds for stochastic Navier-Stokes equations. J. of Math. Anal. and Appl., 196, no. 1, 221-236.

Chueshov I. D. (1995) Approximate inertial manifolds of exponential order for semilinear parabolic equations subjected to additive white noise. J. of Dyn. and Diff. Eqs., 7, no. 4, 549-566.

Chueshov I. D., Rezounenko A. V. (1995) Global attractors for a class of retarded quasilinear partial differential equations. C. R. Acad. Sci. Paris, ser. I, 321, 607-612.

Chueshov I. D., Rezounenko A. V. (1995) Global attractors for a class of retarded quasilinear partial differential equations. Math. Physics, Analysis, Geometry, 1995, 2, no. 3/4, 363-383.

Chueshov I. D. (1995) Approximate inertial manifolds and nonlinear Galerkin method for second order in time initial-boundary problems. Nonlinear Boundary-Value Problems, no. 6, 141-146 (Russian).

1994

Chueshov I .D. (1994) The quasistatic version of system of von Karman equations. Mathematical Physics, Analysis, Geometry, 1, no. 1, 149-167 (Russian).

Chueshov I. D. (1994) Regularity of solutions and approximate inertial manifolds for von Karman evolution equations. Math. Meth. in Appl. Sci., 17, 667-680.

Chueshov I. D., Girya T. V. (1994) Inertial manifolds for stochastic dissipative dynamical systems. Doklady of Acad. Sci. of Ukraine., no. 7, 42-45.

1993

Chueshov I. D. (1993) On a system of equations of parabolic type, that arises in semiconductor physics. Teor. Funktisii, Funktsional. Anal. i Prilozhen., 58, 40-45 (Russian).

Chueshov I. D. (1993) Approximate inertial manifolds for second order evolution equation. Doklady of Acad. Sci. of Ukraine, no. 3, 49-52.

Chueshov I. D. (1993) Global attractors for nonlinear problems of Mathematical Physics. Uspekhi Mat. Nauk, 48., no. 3, 135-162 (Russian); English transl. in Russian Math. Surveys, 48 (1993).

1992

Chueshov I. D. (1992) Introduction to the theory of inertial manifolds (Lecture Notes), Kharkov Univ. Press: Kharkov (Russian).

Chueshov I. D. (1992) On some continuity property of attractor in a problem on oscillations of shallow shell. In: Dynamical systems and complex analysis, Marchenko V. A. (ed.), Naukova dumka: Kiev, 85-91 (Russian).

1991

Chueshov I. D. (1991) Waves in one-dimensional systems. Introduction. (Lecture Notes), Kharkov Univ.Press: Kharkov (Russian).

Chueshov I. D. (1991) The construction of solutions in the problem of shell oscillations in potential subsonic flow. - In: Operator theory, subharmonic functions, Marchenko V. A. (ed.), Naukova dumka: Kiev, 147-154 (Russian).

Chueshov I. D. (1991) The mathematical foundations of nonregular oscillation theory of infinite-dimensional systems (Lecture Notes), Kharkov Univ. Press: Kharkov (Russian).

1990

Chueshov I. D. (1990) Strong solutions and the attractor of the von Karman equation. Matem. Sbornik, 181, no. 1, 25-36 (Russian); English transl. in Math. USSR Sb., 69, (1991).

Chueshov I. D. (1990) A problem on nonlinear oscillations of shallow shell in quasistatic formulation. Matem. Zametki, 47, no. 4, 128-137 (Russian); English transl. in Math. Notes, 47 (1990).

Chueshov I. D. (1990) On a certain system of equations with delay occurring in aeroelasticity. Teor. Funktisii, Funktsional. Anal. i Prilozhen., 54, 123-129 (Russian); English transl. in J. Soviet Math., 58, (1992).

Chueshov I. D. (1990) Inertial manifolds in a problem on nonlinear oscillations of infinite panel. Ukrainian Math. J., 42, no. 9, 1149-1151.

Chueshov I. D. (1990) On the properties of statistical solutions of modified system of von Karman equations. In: Analitical methods in probability theory and operator theory, Marchenko V. A. (ed.), Naukova dumka: Kiev, 137-145 (Russian).

1989

Chueshov I. D. (1989) Asymptotic behavior of the solution of a problem of the aeroelastic oscillations of a shell in hypersonic limit. Teor. Funktisii, Funktsional. Anal. i Prilozhen., 51, 137-141 (Russian); English transl. in J. Soviet Math., 52, no. 6, (1990).

1988

Chueshov I. D. (1988) The properties of an attractor in the problem of nonlinear oscillations of an infinite panel. Teor. Funktisii, Funktsional. Anal. i Prilozhen., 50, 108-115 (Russian); English transl. in J. Soviet Math., 49, no. 6, (1990).

Chueshov I. D. (1988) On the structure of equilibrium state for a class of dynamical systems connected with the Lie-Poisson brackets. Teor. Mat. Fiz., 75, 445-450 (Russian); English transl. in Theor. Math. Phys., 75 (1988).

Chueshov I. D. (1988) Strong solutions and the attractor of the von Karman equation. Doklady Acad. Sci. of Ukraine SSR, ser. A, no.5, 22-24 (Russian).

1987

Chueshov I. D. (1987) On the construction of solutions of stochastic modified system of von Karman equations. - In: Operators in functional spaces and questions of function theory, Marchenko V. A. (ed.), Naukova dumka: Kiev, 32-43 (Russian).

Chueshov I. D. (1987) Finite dimensionality of an attractor in some problems of nonlinear shell theory. Matem. Sbornik, 133(175), no. 4, 419-428 (Russian); English transl. in Math. USSR Sb., 61, (1988).

Chueshov I. D. (1987) Structure of a maximal attractor of a modified system of von Karman equations. Teor. Funktisii, Funktsional. Anal. i Prilozhen., 47, 99-104 (Russian); English transl. in J. Soviet Math., 48, no. 6, (1990).

Chueshov I. D. (1987) Attractor for a problem on forced oscillations of shallow shell. Doklady Acad. Sci. of Ukraine SSR, ser. A, no. 4, 26-28 (Russian).

1986

Chueshov I. D. (1986) Remark on the propagation of chaos theorem. Teor. Mat. Fiz., 67, 304-308 (Russian); English transl. in Theor. Math. Phys., 67 (1986).

Chueshov I .D. (1986) Equilibrium statistical solutions for dynamical systems with an infinite number of degrees of freedom. Matem. Sbornik, 130(172), no.3, 394-403 (Russian); English transl. in Math. USSR Sb., 58, (1987).

Chueshov I. D. (1986) Maximal attractor for a problem on nonlinear oscillations of elastic shallow shells. Uspekhi Mat. Nauk, 41., no. 5, 217-218 (Russian).

1985

Chueshov I. D. (1985) Feynman's integral for the Schrodinger equation with a nonstationary potential. Selecta Math. Sov., 4, no.1, 47-54.

1984

Chueshov I. D. (1984) The Hopf equation for the infinite dimensional phase space dynamical system and Euclidian quantum field theory. Preprint ITP-84-184R of Institute for Theoretical Physics, Kiev (Russian).

1983

Chueshov I. D. (1983) On statistical solutions in nonlinear mechanics of elastic shallow shells. - In: Analysis in infinite dimensional spaces and operator theory, Marchenko V. A. ( ed.), Naukova dumka: Kiev, 139-146 (Russian).

Chueshov I. D. (1983) Remark on non-stable regularizations of the Schrodinger operator with singular repulsive potential. Teor. Funktisii, Funktsional. Anal. i Prilozhen., 39, 125-129 (Russian).

Chueshov I. D. (1983) The existence of statistical solutions for stochastic system of the von Karman equations. Matem. Sbornik, 122(164), no.3, 291-312 (Russian).

1982

Chueshov I. D. (1982) Statistical solutions for stochastic system of the von Karman equations. Doklady Acad. Sci. of Ukraine SSR, ser.A, no.9, 26-29 (Russian).

1981

Chueshov I. D. (1981) Remark on the Schrodinger operator with high-singular potential. Funktsional. Anal. i Prilozhen., 15, no.4, 93-94 (Russian).

Chueshov I. D. (1981) On cores for the Schrodinger operator with high-singular potential. Teor. Funktisii, Funktsional. Anal. i Prilozhen., 36, 111-124 (Russian).

1980

Chueshov I. D. (1980) Stability of regularizations of the many-particle Schrodinger operator with singular repulsive two-body potential. Teor. Mat. Fiz., 43, 57-64 (Russian); English transl. in Theor. Math. Phys.,43 (1980).

Chueshov I. D. (1980) Operator methods in Mathematical Physics. (Lecture Notes), Kharkov Univ. Press: Kharkov (Russian).

1978

Chueshov I. D. (1978) Probability structure of a certain class of S-matrix equations in boson theory. Teor. Mat. Fiz., 37, 30-39 (Russian); English transl. in Theor. Math. Phys., 37 (1978).

Chueshov I. D. (1978) Stability of regularizations of the Schrodinger operator with singular repulsive potential. Teor. Mat. Fiz., 37, 237-242 (Russian); English transl. in Theor. Math. Phys., 37 (1978).

Chueshov I. D. (1978) On weak limiting points of Feynman integral products. Funktsional. Anal. i Prilozhen., 12, no.1, 90-91 (Russian).

1976

Chueshov I. D. (1976) On the Bogoliubov operator S(g) for some two-dimensional quantum field theory models. Teor. Mat. Fiz., 27, 288-296 (Russian); English transl. in Theor. Math. Phys., 27 (1976).

Chueshov I. D. (1976) On perturbation of the Schrodinger equation by potential with small support. Matem. Zametki, 20, no.5, 675-680 (Russian); English transl. in Math. Notes, 20 (1976).

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