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ESAIM: Control, Optimisation and Calculus of Variations (1)

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Analytic controllability of the wave equationover a cylinder
Brice Allibert
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 4 / 1999

Published online by Cambridge University Press:

15 August 2002, pp. 177-207

Print publication:

1999
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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.