Recent Papers
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Local existence theorems with unbounded set of input data and unboundedness of stable invariant manifolds for
3D Navier-Stokes equations.- Discrete and Continuous Dynamical Systems (to appear in 2010)
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Optimal Neumann Control for the 2D Sready-state Navier-Stokes Equations.- New Directions in Mathematical
Fluid Mechanics-The Alexander V. Kazhikhov Memorial Volume, Birkhauser, (to appear in 2009)(with R.Rannacher)
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The Ginzburg-Landau Equations for Superconductivity with Random
Fluctuations. 2008 (with M.D. Gunzburger, J.S. Peterson)
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Analyticity of stable invariant manifolds of 1D-semilinear parabolic
equations.- Proc.of Joint Summer Research Conf.on Control Meth.and
PDE Dynamical Syst.; AMS Contemporary Mathematics (CONM) Series,
Providence, 2007 (to appear)
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Analyticity of stable invariant manifolds for Ginzburg-Landau equation.-
Proceedings of International Conference on Applied Analysis and
Differential Equations, Iasi, September 4-9, 2006. (to appear)
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Homogeneous and Isotropic Statistical Solutions of the Navier-Stokes Equations.-
Math. Physics Electronic Journal,
v.12, paper No. 2, 2006 (with S.Dostoglou, J.D.Kahl)
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Optimal boundary control for
the evolutionary Navier-Stokes system: the three-dimensional
case.- SIAM. J. Control Optim. v.43, \#6, (2005),2191-2232.
(with M. Gunzburger and L. Hou)
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Feedback Stabilization for Oseen Fluid Equations: A Statistical
Approach, J.of Maty. Fluid Mech. 7 (4), (2005), p.p.574-610 (with J.Duan)
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Stabilization for the 3D Navier-Stokes system by feedback boundary control.- Discrete and Cont. Dyn. Syst. v.10 № 1&2, 2004, p.p. 289-314
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Существование решений экстремальных задач. PDF-FILE (2003) (совм. с В.М.Тихомировым)
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Static Hedging of Barrier Options with a Smile: An inverse Problem.-ESAIM, Control, optimization and Calculus of Variations, v.8, 2002, p.p.127-142 (with C. Bardos and R. Douady)
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Стабилизация с границы решений системы Навье-Стокса: разрешимость и обоснование возможности численного моделирования.- Дальневосточный Мат. Ж., т.4, №1 2003 , с. 86-100
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Feedback stabilization for the 2D Oseen equations: additional remarks.- Control and estimation of Distributed Parameter Systems. International series of numerical mathematics. W.Desch, F.Kappel, and K.Kunish, eds., Birkh\"aser Verlag, Basel 2003, p. 169-188.
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Реальные процессы и реализуемость метода стабилизации системы Навье-Стокса посредством управления с обратной связью с границы области,.-Нелинейные задачи математической физики и смежные вопросы. II. В честь О.А.Ладыженской. Междунар. Матем. Серия т.2 . Издательство Т.Рожковской, 2002, с. 127-164
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Real Process Corresponding to 3D Navier-Stokes System and Its Feedback Stabilization from Boundary .- The M.I.Vishik seminar, AMS Translations Serie 2, v.206, (2002) p. 95-123.
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Boundary value problems for three-dimensional evolutionary Navier-Stokes equations.- J. Math. Fluid Mech., vol.4:1 (2002),p.45-75. (with M. Gunzburger and L. Hou)
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Trace theorems for Three-Dimensional, time-dependent solenoidal vector fields and their applications, Trans. Amer.Math. Soc. v.354, (2002), p.1079-1116. (with M.D.Gunzburger,L.S.Hou)
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Feedback stabilization for the 2D Navier-Stokes equations.- The Navier-Stokes equations: theory and numerical methods. Lecture Notes in pure and appl. Math., vol. 223, (2001) Marcel Dekker, Inc., New-York, Basel, pp.179-196.
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Stabilizability of Two-Dimensional Navier-Stokes equations with help of a boundary feedback control.- J. of Math. Fluid Mech. v.3, (2001), 259-301.
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Стабилизируемость квазилинейного параболического уравнения с помощью граничного управления с обратной связью.- Матем. Сб., т. 192, № 4, (2001), с. 115-160.
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Точная управляемость с границы и стабилизация посредством граничного управления с обратной связью для параболических уравнений и системы Навье-Стокса.- Вестник Тамбовск. Университета, т.5, № 4, (2000), с. 509.
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Exact controllability of the Navier-Stokes and Boussinesq equations.- Russia Math. Surveys, Vol. 54, № 3, 1999, с. 93-146. (with O.Yu. Imanuvilov ).
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Controllability property for the Navier-Stokes equations.- Proceedings of the International Conference on Control of Partial Differential Equations. Chemnitz, April 20-25, 1998, International Series of numerical Mathematics, Vol. 133, pp.157-165, 1999 Birkhauser Verlag Basel/Switserland
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The closure problem for the Friedman-Keller infinite chain of moment equations, corresponding to the Navier-Stokes system.- Proceedings of the Second Monte Verita Colloquium on Turbulence, March 22-28, 1998, Trends in Mathematics, 1999, Birkhauser Verlag Bassel/Switzerland, pp.17-24.
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Оптимальное управление распределенными системами. Теория и приложения.- Научная книга. Новосибирск 1999. 350с.
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