Advanced Search
Article Contents
Article Contents

A problem of boundary controllability for a plate

Abstract Related Papers Cited by
  • The boundary controllability problem, here discussed, might be described by a two-dimensional space equation modeling, at the same time $t$, different physical phenomena in a composite solid made of different materials. These phenomena may be governed, at the same time $t$, for example, by the heat equation and by the Schrödinger equation in two separate regions. Interface transmission conditions are imposed.
    Mathematics Subject Classification: 35, 93.


    \begin{equation} \\ \end{equation}
  • [1]

    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.


    O. Arena and W. Littman, Null Boundary Controllability of the Schrödinger Equation with a Potential, Proceedings $7^{th}$ Int. ISAAC Congress (July 2009), Progress in Analysis and its Applications, (M. Ruzhansky and J. Wirth Eds.) 2010.doi: 10.1142/9789814313179_0046.


    G. Avalos and I. Lasiecka, The null controllability of thermo-elastic 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.


    L. Hörmander, Linear Partial Differential Operators, Academic Press, New York, 1963.


    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 Opt., 27 (1989), 330-373.doi: 10.1137/0327018.


    I. Lasiecka and R. Triggiani, Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet control, Differential and Integral Equations, 5 (1992), 521-535.


    W. Littman, Boundary control Theory for Beams and Plates, Proceedings, 24th Conference on Decision and Control, Ft. Lauderdale, FL, 2007-2009, December 1985.doi: 10.1109/CDC.1985.268511.


    W. Littman and S. Taylor, Smoothing Evolution Equations and Boundary control theory. Festschrift on the occasion of the 70th birthday of Shmuel Agmon, Journal d'Analyse. Mathématique, 59 (1992), 117-131.doi: 10.1007/BF02790221.


    W. Littman and S. Taylor, The heat and schrödinger equation boundary control with one shot, Control Methods in PDE-Dynamical Systems, Contemporary Math., 426, AMS, Providence, RI, (2007), 293-305.doi: 10.1090/conm/426/08194.


    W. Littman and S. Taylor, The balayage method: Boundary control of a thermo-elastic plate, Applicationes Math., 35 (2008), 467-479.doi: 10.4064/am35-4-5.


    A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983.doi: 10.1007/978-1-4612-5561-1.


    S. Taylor, Gevrey smoothing properties of the schrödinger evolution group in weighted sobodev spaces, Journal of Math. Anal. and Appl., 194 (1995), 14-38.doi: 10.1006/jmaa.1995.1284.


    F. Trèves, Ovcyannikov Theorem and Hyperdifferential Operators, Notas de Matemática, No. 46 Instituto de Matemática Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro 1968 iii+238 pp.


    X. Zhang and E. Zuazua, Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system, Journal of Diff. Eq., 204 (2004), 380-438.doi: 10.1016/j.jde.2004.02.004.


    E. Zuazua, Null Control of a 1-d Model of Mixed Hyperbolic-Parabolic Type, in: J. L. Menaldi et al., (Eds), Optimal Control and PDE, IOS Press, Amsterdam, 2001.


    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.

  • 加载中

Article Metrics

HTML views() PDF downloads(112) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint