# Analytic controllability of the wave equation over a cylinder

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 4, page 177-207
- ISSN: 1292-8119

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topAllibert, Brice. "Analytic controllability of the wave equation over a cylinder." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 177-207. <http://eudml.org/doc/197336>.

@article{Allibert2010,

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.
},

author = {Allibert, Brice},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Wave equation; attainable set; analyticity; boundary control.; boundary control; wave equation; controllability; observability},

language = {eng},

month = {3},

pages = {177-207},

publisher = {EDP Sciences},

title = {Analytic controllability of the wave equation over a cylinder},

url = {http://eudml.org/doc/197336},

volume = {4},

year = {2010},

}

TY - JOUR

AU - Allibert, Brice

TI - Analytic controllability of the wave equation over a cylinder

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 4

SP - 177

EP - 207

AB -
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.

LA - eng

KW - Wave equation; attainable set; analyticity; boundary control.; boundary control; wave equation; controllability; observability

UR - http://eudml.org/doc/197336

ER -

## References

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- A. Haraux, 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).
- G. Lebeau, Fonctions harmoniques et spectre singulier. Ann. Sci. École Norm. Sup.13 (1980) 269-291.
- 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).

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