Advanced Search
Article Contents
Article Contents

Null controllability of retarded parabolic equations

Abstract Related Papers Cited by
  • We address in this work the null controllability problem for a linear heat equation with delay parameters. The control is exerted on a subdomain and we show how the global Carleman estimate due to Fursikov and Imanuvilov can be applied to derive results in this direction.
    Mathematics Subject Classification: 93B05, 93B07, 47D06, 34K35, 35K10, 35R10.


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

    F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. González-Burgos, A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems, J. Evol. Equ., 9 (2009), 267-291. Available from: http://hal.archives-ouvertes.fr/hal-00290867/fr/.doi: 10.1007/s00028-009-0008-8.


    F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. González-Burgos, Controllability for a class of reaction-diffusion systems: The generalized Kalman's condition, C. R. Math. Acad. Sci. Paris, 345 (2007), 543-548.doi: 10.1016/j.crma.2007.10.023.


    F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. González-Burgos, A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems, Differ. Equ. Appl., 1 (2009), 427-457.doi: 10.7153/dea-01-24.


    F. Ammar-Khodja, A. Benabdallah, M. González-Burgos and L. de Teresa, The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials, J. Math. Pures Appl. (9), 96 (2011), 555-590. Available from: http://hal.archives-ouvertes.fr/hal-00539825/fr/.doi: 10.1016/j.matpur.2011.06.005.


    M. Artola, Sur les perturbations des équations d'évolution: Application à des problèmes avec retard, Ann. Sci. École Norm. Sup. (4), 2 (1969), 137-253.


    V. Barbu, Exact controllability of the superlinear heat equation, Appl. Math. Optim., 42 (2000), 73-89.doi: 10.1007/s002450010004.


    R. F. Curtain and H. 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.


    E. Fernández-Cara, M. González-Burgos and L. de Teresa, Boundary controllability of parabolic coupled equations, J. Funct. Anal., 259 (2010), 1720-1758.doi: 10.1016/j.jfa.2010.06.003.


    E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations, Ann. Inst. H. Poincaré, Anal. Non Linéaire, 17 (2000), 583-616.doi: 10.1016/S0294-1449(00)00117-7.


    A. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series, 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, Korea, 1996.


    S.-I. Nakagiri, Optimal control of linear retarded systems in Banach spaces, J. Math. Anal. and Appl., 120 (1986), 169-210.doi: 10.1016/0022-247X(86)90210-6.


    S.-I. Nakagiri and M. Yamamoto, Controllability and observability of linear retarded systems in Banach spaces, Int. J. Control, 49 (1989), 1489-1504.


    J. Zabczyk, Mathematical Control Theory: An Introduction, Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 1992.

  • 加载中

Article Metrics

HTML views() PDF downloads(208) Cited by(0)

Access History



    DownLoad:  Full-Size Img  PowerPoint