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Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension
1. | T.I.F.R Centre for Applicable Mathematics, Post Bag No. 6503, GKVK Post Oce, Bangalore-560065, India, India |
2. | Institut de Mathématiques de Toulouse, Université Paul Sabatier & CNRS, 31062 Toulouse Cedex, France |
References:
[1] |
E. V. Amosova, Exact local controllability for the equations of viscous gas dynamics, Differential Equations, 47 (2011), 1776-1795.
doi: 10.1134/S001226611112007X. |
[2] |
A. Bensoussan, G. Da Prato, M. Delfour and S. K. Mitter, Representation and Control of Infinite Dimensional Systems, Second edition, Systems and Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 2007.
doi: 10.1007/978-0-8176-4581-6. |
[3] |
S. Chowdhury, M. Ramaswamy and J.-P. Raymond, Controllability and stabilizability of the linearized compressible Navier-Stokes system in one dimension, SIAM J. Control Optim., 50 (2012), 2959-2987.
doi: 10.1137/110846683. |
[4] |
S. Chowdhury, D. Maity, M. Ramaswamy and J.-P. Raymond, Local stabilization of the compressible Navier-Stokes system, around a null velocity, in one dimension, to appear in J. Differential Equations.
doi: 10.1016/j.jde.2015.02.025. |
[5] |
S. Chowdhury and D. Mitra, Null controllability for linearized compressible Navier-Stokes equations by moment method, J. Evol. Equ., (2014).
doi: 10.1007/s00028-014-0263-1. |
[6] |
S. Chowdhury, D. Mitra, M. Ramaswamy and M. Renardy, Null controllability of the linearized compressible Navier-Stokes system in one dimension, J. Differential Equations, 257 (2014), 3813-3849.
doi: 10.1016/j.jde.2014.07.010. |
[7] |
R. F. Curtain and H. J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts in Applied Mathematics, 21, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4224-6. |
[8] |
S. Ervedoza, O. Glass, S. Guerrero and J.-P. Puel, Local exact controllability for the one-dimensional compressible Navier-Stokes equation, Arch. Rational Mech. Anal., 206 (2012), 189-238.
doi: 10.1007/s00205-012-0534-3. |
[9] |
S. Kesavan and J.-P. Raymond, On a degenerate Riccati equation, Control Cybernet., 38 (2009), 1393-1410. |
[10] |
G. Lebeau and E. Zuazua, Null-controllability of a system of linear thermoelasticity, Arch. Rational Mech. Anal., 141 (1998), 297-329.
doi: 10.1007/s002050050078. |
[11] |
D. Mitra, M. Ramaswamy and J.-P. Raymond, Local stabilization of compressible Navier-Stokes equations in one dimension around non-zero velocity, submitted. |
[12] |
J. Zabczyk, Mathematical Control Theory. An Introduction, Reprint of the 1995 edition, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008.
doi: 10.1007/978-0-8176-4733-9. |
[13] |
K. Zhou, J. C. Doyle and K. Glover, Robust and Optimal Control, Prentice Hall, Englewood Cliffs, New Jersey, 1995. |
show all references
References:
[1] |
E. V. Amosova, Exact local controllability for the equations of viscous gas dynamics, Differential Equations, 47 (2011), 1776-1795.
doi: 10.1134/S001226611112007X. |
[2] |
A. Bensoussan, G. Da Prato, M. Delfour and S. K. Mitter, Representation and Control of Infinite Dimensional Systems, Second edition, Systems and Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 2007.
doi: 10.1007/978-0-8176-4581-6. |
[3] |
S. Chowdhury, M. Ramaswamy and J.-P. Raymond, Controllability and stabilizability of the linearized compressible Navier-Stokes system in one dimension, SIAM J. Control Optim., 50 (2012), 2959-2987.
doi: 10.1137/110846683. |
[4] |
S. Chowdhury, D. Maity, M. Ramaswamy and J.-P. Raymond, Local stabilization of the compressible Navier-Stokes system, around a null velocity, in one dimension, to appear in J. Differential Equations.
doi: 10.1016/j.jde.2015.02.025. |
[5] |
S. Chowdhury and D. Mitra, Null controllability for linearized compressible Navier-Stokes equations by moment method, J. Evol. Equ., (2014).
doi: 10.1007/s00028-014-0263-1. |
[6] |
S. Chowdhury, D. Mitra, M. Ramaswamy and M. Renardy, Null controllability of the linearized compressible Navier-Stokes system in one dimension, J. Differential Equations, 257 (2014), 3813-3849.
doi: 10.1016/j.jde.2014.07.010. |
[7] |
R. F. Curtain and H. J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts in Applied Mathematics, 21, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4224-6. |
[8] |
S. Ervedoza, O. Glass, S. Guerrero and J.-P. Puel, Local exact controllability for the one-dimensional compressible Navier-Stokes equation, Arch. Rational Mech. Anal., 206 (2012), 189-238.
doi: 10.1007/s00205-012-0534-3. |
[9] |
S. Kesavan and J.-P. Raymond, On a degenerate Riccati equation, Control Cybernet., 38 (2009), 1393-1410. |
[10] |
G. Lebeau and E. Zuazua, Null-controllability of a system of linear thermoelasticity, Arch. Rational Mech. Anal., 141 (1998), 297-329.
doi: 10.1007/s002050050078. |
[11] |
D. Mitra, M. Ramaswamy and J.-P. Raymond, Local stabilization of compressible Navier-Stokes equations in one dimension around non-zero velocity, submitted. |
[12] |
J. Zabczyk, Mathematical Control Theory. An Introduction, Reprint of the 1995 edition, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008.
doi: 10.1007/978-0-8176-4733-9. |
[13] |
K. Zhou, J. C. Doyle and K. Glover, Robust and Optimal Control, Prentice Hall, Englewood Cliffs, New Jersey, 1995. |
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