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On Kelvin-Voigt model and its generalizations
Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension
1. | Octav Mayer Institute of Mathematics (Romanian Academy), Bd. Carol I, no. 8, Iaşi 700505, Romania |
2. | Octav Mayer Institute of Mathematics (Romanian Academy), and Alexandru Ioan Cuza University (Department of Mathematics), Bd. Carol I, no. 8, Iaşi 700505, Romania |
References:
[1] |
A. V. Balakrishanan, "Applied Functional Analysis,", Second editon, 3 (1981).
|
[2] |
V. Barbu, Feedback stabilization of Navier-Stokes equations,, ESAIM COCV, 9 (2003), 197.
doi: 10.1051/cocv:2003009. |
[3] |
V. Barbu and R. Triggiani, Internal stabilization of Navier-Stokes equations with finite dimensional controllers,, Indiana Univ. Math. Journal, 53 (2004), 1443.
doi: 10.1512/iumj.2004.53.2445. |
[4] |
V. Barbu, I. Lasiecka and R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations,, Memoires AMS, 851 (2006).
|
[5] |
V. Barbu, R. Triggiani and I. Lasiecka, Abstract settings for tangential boundary stabilization of Navier-Stokes equations by high and low-gain feedback controllers,, Nonlin. Anal., 64 (2006), 2704.
doi: 10.1016/j.na.2005.09.012. |
[6] |
V. Barbu, Optimal stabilizable feedback controller for Navier-Stokes equations,, in, 513 (2010), 43.
|
[7] |
V. Barbu and C. Lefter, Internal stabilizability of the Navier-Stokes equations. Optimization and control of distributed systems,, Systems and Control Letters, 48 (2003), 161.
doi: 10.1016/S0167-6911(02)00261-X. |
[8] |
V. Barbu, "Stabilization of the Navier-Stokes Flows,", Springer, (2010). |
[9] |
V. Barbu, I. Lasiecka and R. Triggiani, The unique continuation property of eigenfunctions to Stokes-Oseen operator is generic with respect to the coefficients,, Nonlin. Anal. Ser. A: Theory Meth. and Appl., (). |
[10] |
M. Bedra, Feedback stabilization of the 2-D and 3-D Navier Stokes equations based on an extended system,, ESAIM COCV, 15 (2009), 934.
doi: 10.1051/cocv:2008059. |
[11] |
M. Bedra, Lyapunov functions and local feedback stabilization of the Navier-Stokes equations,, SIAM J. Control Optimiz., 48 (2009), 1797.
doi: 10.1137/070682630. |
[12] |
J.-M. Coron, "Control and Nonlinearity,", Mathematical Surveys and Monographs, 136 (2007).
|
[13] |
A. Fursikov, Stabilization for the 3D Navier-Stokes systems by feedback boundary control,, Discrete and Contin. Dyn. Syst., 10 (2004), 289.
doi: 10.3934/dcds.2004.10.289. |
[14] |
I. Lasiecka and R. Triggiani, "Control Theory for Partial Differential Equations: Continuous and Approximation Theory,", Cambridge Univ. Press, (2000). |
[15] |
J.-P. Raymond, Feedback boundary stabilization of the three-dimensional incompressible Navier-Stokes equations,, J. Math. Pures et Appl. (9), 87 (2007), 627.
doi: 10.1016/j.matpur.2007.04.002. |
[16] |
S. S. Ravindran, Reduced-order adaptive controllers for fluid flows using POD,, J. Scientific Computing, 15 (2000), 457.
|
[17] |
A. Shirikyan, Exact controllability in projections for three-dimensional Navier-Stokes equations,, Ann. I. H. Poincaré Anal. Non Linéaire, 24 (2007), 521.
|
[18] |
P. Constantin and C. Foias, "Navier-Stokes Equations,", Chicago Lectures in Mathematics, (1988).
|
show all references
References:
[1] |
A. V. Balakrishanan, "Applied Functional Analysis,", Second editon, 3 (1981).
|
[2] |
V. Barbu, Feedback stabilization of Navier-Stokes equations,, ESAIM COCV, 9 (2003), 197.
doi: 10.1051/cocv:2003009. |
[3] |
V. Barbu and R. Triggiani, Internal stabilization of Navier-Stokes equations with finite dimensional controllers,, Indiana Univ. Math. Journal, 53 (2004), 1443.
doi: 10.1512/iumj.2004.53.2445. |
[4] |
V. Barbu, I. Lasiecka and R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations,, Memoires AMS, 851 (2006).
|
[5] |
V. Barbu, R. Triggiani and I. Lasiecka, Abstract settings for tangential boundary stabilization of Navier-Stokes equations by high and low-gain feedback controllers,, Nonlin. Anal., 64 (2006), 2704.
doi: 10.1016/j.na.2005.09.012. |
[6] |
V. Barbu, Optimal stabilizable feedback controller for Navier-Stokes equations,, in, 513 (2010), 43.
|
[7] |
V. Barbu and C. Lefter, Internal stabilizability of the Navier-Stokes equations. Optimization and control of distributed systems,, Systems and Control Letters, 48 (2003), 161.
doi: 10.1016/S0167-6911(02)00261-X. |
[8] |
V. Barbu, "Stabilization of the Navier-Stokes Flows,", Springer, (2010). |
[9] |
V. Barbu, I. Lasiecka and R. Triggiani, The unique continuation property of eigenfunctions to Stokes-Oseen operator is generic with respect to the coefficients,, Nonlin. Anal. Ser. A: Theory Meth. and Appl., (). |
[10] |
M. Bedra, Feedback stabilization of the 2-D and 3-D Navier Stokes equations based on an extended system,, ESAIM COCV, 15 (2009), 934.
doi: 10.1051/cocv:2008059. |
[11] |
M. Bedra, Lyapunov functions and local feedback stabilization of the Navier-Stokes equations,, SIAM J. Control Optimiz., 48 (2009), 1797.
doi: 10.1137/070682630. |
[12] |
J.-M. Coron, "Control and Nonlinearity,", Mathematical Surveys and Monographs, 136 (2007).
|
[13] |
A. Fursikov, Stabilization for the 3D Navier-Stokes systems by feedback boundary control,, Discrete and Contin. Dyn. Syst., 10 (2004), 289.
doi: 10.3934/dcds.2004.10.289. |
[14] |
I. Lasiecka and R. Triggiani, "Control Theory for Partial Differential Equations: Continuous and Approximation Theory,", Cambridge Univ. Press, (2000). |
[15] |
J.-P. Raymond, Feedback boundary stabilization of the three-dimensional incompressible Navier-Stokes equations,, J. Math. Pures et Appl. (9), 87 (2007), 627.
doi: 10.1016/j.matpur.2007.04.002. |
[16] |
S. S. Ravindran, Reduced-order adaptive controllers for fluid flows using POD,, J. Scientific Computing, 15 (2000), 457.
|
[17] |
A. Shirikyan, Exact controllability in projections for three-dimensional Navier-Stokes equations,, Ann. I. H. Poincaré Anal. Non Linéaire, 24 (2007), 521.
|
[18] |
P. Constantin and C. Foias, "Navier-Stokes Equations,", Chicago Lectures in Mathematics, (1988).
|
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