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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), 12-17. |
[2] |
O. Arena, A problem of boundary controllability for a plate, Evol. Equ. and Control Theory, 2 (2013), 557-562.
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), 431-437.
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, World Sci. Publ., Hackensack, NJ, 2010, 357-362.
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), 34-61.
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, Springer-Verlag, New York Inc., 1984.
doi: 10.1007/978-1-4612-5208-5. |
[7] |
L. Hörmander, Linear Partial Differential Operators, Academy Press, New York, 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), 330-373.
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), 521-535. |
[10] |
W. Littman, Boundary control theory for beams and plates, in Proceedings, 24th Conference on Decision and Control, Ft. Lauderdale, FL, (1985), 2007-2009.
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), 117-131.
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, Contemp. Math., 426, Amer. Math. Soc., Providence, RI (2007), 293-305.
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), 467-479.
doi: 10.4064/am35-4-5. |
[14] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[15] |
I. N. Sneddon, Fourier Transforms, Dover Publ. inc., New York, 1995. |
[16] |
S. Taylor, Gevrey smoothing properties of the Schrödinger evolution group in weighted Sobodev spaces, J. Math. Anal. Appl., 194 (1985), 14-38.
doi: 10.1006/jmaa.1995.1284. |
[17] |
F. Trèves, Ovcyannikov Theorem and Hyperdifferential Operators, Notas de Matemática, 46, Instituto de Matemática Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1968. |
[18] |
X. Zhang and E. Zuazua, Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system, J. Differential Equations, 204 (2004), 380-438.
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.), IOS Press, Amsterdam, 2001. |
show all references
References:
[1] |
O. Arena, Some problems on boundary controllability for PDE's, Boll. Acad. Gioenia (CT), 46 (2013), 12-17. |
[2] |
O. Arena, A problem of boundary controllability for a plate, Evol. Equ. and Control Theory, 2 (2013), 557-562.
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), 431-437.
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, World Sci. Publ., Hackensack, NJ, 2010, 357-362.
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), 34-61.
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, Springer-Verlag, New York Inc., 1984.
doi: 10.1007/978-1-4612-5208-5. |
[7] |
L. Hörmander, Linear Partial Differential Operators, Academy Press, New York, 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), 330-373.
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), 521-535. |
[10] |
W. Littman, Boundary control theory for beams and plates, in Proceedings, 24th Conference on Decision and Control, Ft. Lauderdale, FL, (1985), 2007-2009.
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), 117-131.
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, Contemp. Math., 426, Amer. Math. Soc., Providence, RI (2007), 293-305.
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), 467-479.
doi: 10.4064/am35-4-5. |
[14] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[15] |
I. N. Sneddon, Fourier Transforms, Dover Publ. inc., New York, 1995. |
[16] |
S. Taylor, Gevrey smoothing properties of the Schrödinger evolution group in weighted Sobodev spaces, J. Math. Anal. Appl., 194 (1985), 14-38.
doi: 10.1006/jmaa.1995.1284. |
[17] |
F. Trèves, Ovcyannikov Theorem and Hyperdifferential Operators, Notas de Matemática, 46, Instituto de Matemática Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1968. |
[18] |
X. Zhang and E. Zuazua, Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system, J. Differential Equations, 204 (2004), 380-438.
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.), IOS Press, Amsterdam, 2001. |
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