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Analytic controllability of the wave equation over 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

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