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[1] J.-L. Lions, Are the connections between turbulence and controllability?, Lecture Notes in Control Inform. Sci., V (1990), 144.
[2] J.-L. Lions, Remarques sur la controllabilite approchee, Control of Distributed Systems, 3 (1990), 7787.
[3] . . , .. , -, . ., 187:9 (1996), 102138.
[4] . . , .. , , . , . ., 3:1 (1996), 177194.
[5] . . , .. , - , , 54:3(327) (1999), 9342.
[6] A. V. Fursikov, O.Yu. Imanuvilov, Local exact controllability of the Navier-Stokes equations, C. R. Acad. Sci., Paris, Serie I., 323 (1996), 275280.
[7] A. V. Fursikov, O.Yu. Imanuvilov, Local Exact Boundary Controllability of the Boussinesque Equations, SIAM J. Control Optim., 36:2 (1998), 391421.
[8] A. V. Fursikov, O.Yu. Imanuvilov, On controllability of certain systems simulating a fluid flow, IMA Vol.Math.Appl., 68 (1995), 149184.
[9] O.Yu. Imanuvilov, Local exact controllability for the 2-D Navier-Stokes equations with the Navier slip boundary conditions, Turbulence Modeling and Vortex Dynamics. Lecture Notes in Physics., 491 (1997), 148168.
[10] A. V. Fursikov, O.Yu. Imanuvilov, On exact boundary zero-controllability of two-dimensional Navier-Stokes equations, Acta Appl. Math., 37 (1994), 6776.
[11] J. I Diaz, A. V. Fursikov, Approximate controllability of the Stokes system on cylinders by external unidirectional forces, J. Math. Pures Appl., 76 (1997), 353375.
[12] C. Fabre, J.-P. Puel, E Zuazua, Approximate controllability of the semilinear heat equation, Proc. Roy.Edinburgh. Sect.A., 125 (1995), 3161.
[13] L.A Fernandez, E. Zuazua, Approximate controllability of the semilinear heat equation involving gradient terms, J. Optim. Theory Appl., 1999.
[14] .. , , . . . . ., 1 (1994), 109116.
[15] .. , , , 44:6 (1988), 183184.
[16] O.Yu. Imanuvilov, Local exact controllability for the 2-D Navier-Stokes equations with the Navier slip boundary conditions, Lecture Notes in Phys., 491 (1997), 148168.
[17] . . , . , , ., 1999.
[18] S. Ervedoza, O. Glass O., S. Guerrero, Local exact controllability for the 1-D compressible Navier-Stokes equation, Seminaire Laurent Schwarts - EDP et applications, XXXIX (2011), 14.
[19] E. V. Amosova, Exact Local Controllability for the Equations of Viscous Gas Dynamics, Differential Equations, 47:12 (2011), 17761795.
[20] J.-M. Coron, On the controllability of 2-D incompressible perfect fluids, J. Math. Pures et Appl., 75 (1996), 155188.
[21] J.-M. Coron, Controlabilite exacte frontiere de lequation dEuler des fluides parfaits incompressibles bidimensionnels, C. R. Acad. Sci. Paris. Ser. I., 317 (1993), 271276.
[22] J.-M. Coron, A. V. Fursikov, Global exact controllability of the 2D Navier-Stokes equations on manifold without boundary, Russian Journal of Math. Physics., 4:3 (1996), 120.
[23] V. Barbu, Exact controllability of superlinear heat equation, Applied Mathematics and Optimization, 42 (2000), 7389.
[24] V. Barbu, Controllability of parabolic and Navier-Stokes equations, Scientiae Mathematicae Japonicae, 56 (2002), 143-211.
[25] C. Bardos, G. Lebeau, J. Rauch, Controle et stabilisation de lequation des ondes, SIAM Journal on Control and Optimization, 30 (1992), 10241065.
[26] E. Fernandez-Cara, Null controllability of the semilinear heat equation, ESAIM: Control Optimization and Calculus of Variations, 2 (1997), 87103.
[27] G. Aniculaesei, S. Anita, Null controllability of a nonlinear heat equation, Abstract and Applied Analysis, 7 (2002), 375383.
[28] J. Klamka, Constrained controllability of semilinear systems with multiple delays in control, Bulletin of the Polish Academy of Sciences. Technical Sciences, 52 (2004), 2530.
[29] K. Sakthivel, K. Balachandran, B. R. Nagaraj, On a class of nonlinear parabolic control systems with memory effects, International Journal of Control, 81 (2008), 764777.
[30] K. Sakthivel, K. Balachandran, S. S. Sritharan, Exact controllability of nonlinear diffusion equations arising in reactor dynamics, Nonlinear Analysis:Real World Applications, 9 (2008), 20292054.
[31] A. Kazemi, M. Klibanov, Stability estimates for ill-posed Cauchy problems involving hyperbolic equations and inequalities, Appl. Anal., 50 (1993), 93102.
[32] I. Lasiecka I, R. Triggiani, Carleman estimates and exact boundary controllability for a system of coupled, nonconservative second-order hyperbolic equations, Lecture Notes in Pure Appl. Math., 188 (1997), 215243.
[33] C. Fabre, Uniqueness results for Stokes equations and theirconsequences in linear and nonlinear control problems, ESAIM, Control Optim. Caic. Var., 1 (1996), 267302.
[34] O.Yu. Imanuvilov, M. Yamamoto, On Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations, Publ. Res. Inst. Math. Sci., 39 (2003), 227274.
[35] A. Ruiz, Unique continuation for weak solutions of the wave equation plus a potential, J. Math. Pures Appl., 71 (1992), 455467.
[36] D. Tatary, A prior estimates of Carlemans type in domains with boundary, J. Math. Pures Appl., 73 (1994), 355387.
[37] D. Chae, O.Yu. Imanuvilov, S. M. Kim, Exact controllability for semilinear parabolic equations with Neumann boundary conditions, J. of Dynamical and Control Systems, 2 (1996), 449483.
[38] K. Sakthivel, G. Devipriya, K. Balachandran, J.-H. Kim, Exact null controllability of a semilinear parabolic equation arising in finance, Nonlinear Analysis: Hybrid Systems, 3 (2009), 565577.
[39] .-. , . , , , ., 1971.