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Analytic controllability of the wave equationover a cylinder

Published online by Cambridge University Press:  15 August 2002

Brice Allibert
Brice Allibert*
Affiliation:
CMAT, École Polytechnique, UMR 7640 du CNRS, F-91128 Palaiseau, France; allibert@math.polytechnique.fr.
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Abstract

We analyze the controllability of the wave equation on a cylinder when the control acts on the boundary, that does not satisfy the classical geometric control condition.We obtain precise estimates on the analyticity of reachable functions.As the control time increases, the degree of analyticity that is required for a function to be reachable decreases as an inverse power of time. We conclude that any analytic function can be reached if that control time is large enough. In the C ∞ class, a precise description of all reachable functions is given.

Keywords

Wave equationattainable setanalyticityboundary control.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 177 - 207
Copyright
© EDP Sciences, SMAI, 1999

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References

Allibert, B., Contrôle analytique de l'équation des ondes sur des surfaces de révolution. C. R. Acad. Sci. Paris 322 (1996) 835-838.
B. Allibert, Contrôle analytique de l'équation des ondes sur des surfaces de révolution. Thèse de doctorat de l'École Polytechnique (1997).
Haraux, A., Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire. J. Math. Pures Appl. 68 (1989) 457-465.
G. Lebeau, Control for hyperbolic equations. Journées ``équations aux dérivées partielles'' Saint Jean de Monts, 1992. École Polytechnique, Palaiseau (1992).
Lebeau, G., Fonctions harmoniques et spectre singulier. Ann. Sci. École Norm. Sup. 13 (1980) 269-291. CrossRef
J.-L. Lions, Contrôlabilité exacte, perturbation et stabilisation des systèmes distribués. Rech. Math. Appl. 8-9 (Masson, Paris, 1988).
F. Treves, Introduction to pseudodifferential and Fourier integral operators, New York and London Plenum Press Vol. 2, 25 cm (The university series in mathematics, 1980).
A. Zygmund, Trigonometric Series, Cambridge Univ. Press (1968).