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Null controllability of retarded parabolic equations

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  • 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.

    Citation:

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  • [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.

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    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.

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    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.

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