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Preface to the special issue in memory of Alfredo Lorenzi
On some boundary control problems
1. | Università degli Studi di Firenze, piazza Brunelleschi 6, 50121 Firenze, Italy |
References:
[1] |
O. Arena, Some problems on boundary controllability for PDE's,, Boll. Acad. Gioenia (CT), 46 (2013), 12. Google Scholar |
[2] |
O. Arena, A problem of boundary controllability for a plate,, Evol. Equ. and Control Theory, 2 (2013), 557.
doi: 10.3934/eect.2013.2.557. |
[3] |
O. Arena and W. Littman, Boundary control of two PDE's separated by interface conditions,, J. Syst. Sci. Complex, 23 (2010), 431.
doi: 10.1007/s11424-010-0138-7. |
[4] |
O. Arena and W. Littman, Null boundary controllability of the Schrödinger equation with a potential,, in Progress in Analys and its applications, (2010), 357.
doi: 10.1142/9789814313179_0046. |
[5] |
G. Avalos and I. Lasiecka, The null controllability of thermoelastic plates and singularity of the associated minimal energy function,, J. Math. Anal. Appl., 294 (2004), 34.
doi: 10.1016/j.jmaa.2004.01.035. |
[6] |
J. L. Doob, Classical Potential Theory and Its Probabilistic Counterpart,, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 262, 262 (1984).
doi: 10.1007/978-1-4612-5208-5. |
[7] |
L. Hörmander, Linear Partial Differential Operators,, Academy Press, (1963).
|
[8] |
I. Lasiecka and R. Triggiani, Exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumann boundary conditions, a non conservative case,, SIAM J. Control Optim., 27 (1989), 330.
doi: 10.1137/0327018. |
[9] |
I. Lasiecka and R. Triggiani, Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet control,, Differential Integral Equations, 5 (1992), 521.
|
[10] |
W. Littman, Boundary control theory for beams and plates,, in Proceedings, (1985), 2007.
doi: 10.1109/CDC.1985.268511. |
[11] |
W. Littman and S. Taylor, Smoothing evolution equations and boundary control theory, Festschrift on the occasion of the $70^{th}$ birthday of Samuel Agmon,, Journal d'Analyse. Mathématique, 59 (1992), 117.
doi: 10.1007/BF02790221. |
[12] |
W. Littman and S. Taylor, The heat and Schrödinger equation: Boundary control with one shot,, in Control Methods in PDE-Dynamical Systems, (2007), 293.
doi: 10.1090/conm/426/08194. |
[13] |
W. Littman and S. Taylor, The Balayage method: Boundary control of a thermo-elastic plate,, Appl. Math. (Warsaw), 35 (2008), 467.
doi: 10.4064/am35-4-5. |
[14] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Applied Mathematical Sciences, 44 (1983).
doi: 10.1007/978-1-4612-5561-1. |
[15] |
I. N. Sneddon, Fourier Transforms,, Dover Publ. inc., (1995).
|
[16] |
S. Taylor, Gevrey smoothing properties of the Schrödinger evolution group in weighted Sobodev spaces,, J. Math. Anal. Appl., 194 (1985), 14.
doi: 10.1006/jmaa.1995.1284. |
[17] |
F. Trèves, Ovcyannikov Theorem and Hyperdifferential Operators,, Notas de Matemática, 46 (1968).
|
[18] |
X. Zhang and E. Zuazua, Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system,, J. Differential Equations, 204 (2004), 380.
doi: 10.1016/j.jde.2004.02.004. |
[19] |
E. Zuazua, Null control of a 1-d model of mixed hyperbolic-Parabolic Type,, in: Optimal Control and PDE (eds. J.L. Menaldi et al.), (2001). Google Scholar |
show all references
References:
[1] |
O. Arena, Some problems on boundary controllability for PDE's,, Boll. Acad. Gioenia (CT), 46 (2013), 12. Google Scholar |
[2] |
O. Arena, A problem of boundary controllability for a plate,, Evol. Equ. and Control Theory, 2 (2013), 557.
doi: 10.3934/eect.2013.2.557. |
[3] |
O. Arena and W. Littman, Boundary control of two PDE's separated by interface conditions,, J. Syst. Sci. Complex, 23 (2010), 431.
doi: 10.1007/s11424-010-0138-7. |
[4] |
O. Arena and W. Littman, Null boundary controllability of the Schrödinger equation with a potential,, in Progress in Analys and its applications, (2010), 357.
doi: 10.1142/9789814313179_0046. |
[5] |
G. Avalos and I. Lasiecka, The null controllability of thermoelastic plates and singularity of the associated minimal energy function,, J. Math. Anal. Appl., 294 (2004), 34.
doi: 10.1016/j.jmaa.2004.01.035. |
[6] |
J. L. Doob, Classical Potential Theory and Its Probabilistic Counterpart,, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 262, 262 (1984).
doi: 10.1007/978-1-4612-5208-5. |
[7] |
L. Hörmander, Linear Partial Differential Operators,, Academy Press, (1963).
|
[8] |
I. Lasiecka and R. Triggiani, Exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumann boundary conditions, a non conservative case,, SIAM J. Control Optim., 27 (1989), 330.
doi: 10.1137/0327018. |
[9] |
I. Lasiecka and R. Triggiani, Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet control,, Differential Integral Equations, 5 (1992), 521.
|
[10] |
W. Littman, Boundary control theory for beams and plates,, in Proceedings, (1985), 2007.
doi: 10.1109/CDC.1985.268511. |
[11] |
W. Littman and S. Taylor, Smoothing evolution equations and boundary control theory, Festschrift on the occasion of the $70^{th}$ birthday of Samuel Agmon,, Journal d'Analyse. Mathématique, 59 (1992), 117.
doi: 10.1007/BF02790221. |
[12] |
W. Littman and S. Taylor, The heat and Schrödinger equation: Boundary control with one shot,, in Control Methods in PDE-Dynamical Systems, (2007), 293.
doi: 10.1090/conm/426/08194. |
[13] |
W. Littman and S. Taylor, The Balayage method: Boundary control of a thermo-elastic plate,, Appl. Math. (Warsaw), 35 (2008), 467.
doi: 10.4064/am35-4-5. |
[14] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Applied Mathematical Sciences, 44 (1983).
doi: 10.1007/978-1-4612-5561-1. |
[15] |
I. N. Sneddon, Fourier Transforms,, Dover Publ. inc., (1995).
|
[16] |
S. Taylor, Gevrey smoothing properties of the Schrödinger evolution group in weighted Sobodev spaces,, J. Math. Anal. Appl., 194 (1985), 14.
doi: 10.1006/jmaa.1995.1284. |
[17] |
F. Trèves, Ovcyannikov Theorem and Hyperdifferential Operators,, Notas de Matemática, 46 (1968).
|
[18] |
X. Zhang and E. Zuazua, Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system,, J. Differential Equations, 204 (2004), 380.
doi: 10.1016/j.jde.2004.02.004. |
[19] |
E. Zuazua, Null control of a 1-d model of mixed hyperbolic-Parabolic Type,, in: Optimal Control and PDE (eds. J.L. Menaldi et al.), (2001). Google Scholar |
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