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Recent Papers
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On one estimate, connected with the stabilization of normal parabolic equation by
starting control.-Fundamental and applied mathematics (in Russian, to appear) (with L.S.Shatina) |
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Stabilization of the simplest normal parabolic equation by starting control.
Communication on Pure and Applied Analysis, v.13,N 5,September (2014),1815-1854.
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On the Normal-type Parabolic System Corresponding to the
three-dimensional Helmholtz System.- Advances in Mathematical Analysis of PDEs.
Proc.St.Petersburg Math.Soc. v.XV; AMS Transl.Series 2, v.232 (2014), 99-118.
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Certain questions of feedback stabilization for Navier-Stokes equations.-Evolution equations and control theory (EECT), v.1, N1, 2012, p.109-140 (with A.V.Gorshkov).
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Feedback stabilization for Navier-Stokes equations: theory and calculations.-Proceedings volume "Mathematical Aspects of Fluid Mechanics", edited by J.C. Robinson, J.L. Rodrigo, W. Sadowski (LMS Lecture Notes Series),v.402, Cambridge University Press , 2012, p. 130-172(with
A.A.Kornev).
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Overflow of a body with viscous incompressible fluid: boundary value problems and fluid's work reduction.- Modern mathematics. Fundamental directions. v.37 (2010), p.83–130 (in Russian).
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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 System, Series S, v.3, N 2, (2010), p. 269-290.
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Optimal Neumann Control for the Two-dimensional Steady-state Navier-Stokes equations.- "`New Directions in Mathematical Fluid Mechanics"' (The Alexander V.Kazhikhov memorial volume), Advances in Mathematical Fluid Mechanics, Birkhauser Verlag Basel/Switzerland, 2010, p.193-221. (with R.Rannacher)
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The Ginzburg-Landau Equations for superconductivity with Random Fluctuations.-Sobolev Spaces in Mathematics III. Applications in Mathematical Physics. International Mathematical
Series, v.10, Springer 2008, p.25-134. (with M.Gunsburger, J.Peterson)
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Analyticity of stable invariant manifolds of 1D-semilinear parabolic
equations.- Proceedings of Joint Summer Research Conference on Control Methods and PDE Dynamical Systems, F.Ancona, I.Lasiecka, W.Littman, R.Triggiani (eds.);
AMS Contemporary Mathematics (CONM) Series 426, Providence, 2007, 219-242
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Analyticity of stable invariant manifolds for Ginzburg-Landau equation.-
Applied Analysis and Differential Equations, Iasi, September 4-9, 2006, World Scientific,
2007, 93-112.
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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, N6, (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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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 уравнений Навье-Стокса и Буссинеска.- УМН, т.54, № 3 (327), 1999, с. 93-146. (совм. с О.Ю.Эмануиловым).
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