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analyse spectrale.

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

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Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique
Francis Conrad, Fatima-Zahra Saouri
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 7 / 2002

Published online by Cambridge University Press:

15 September 2002, pp. 567-595

Print publication:

2002
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We study the stability of a flexible beam clamped at one end. A mass is attached at the other end, where a control moment is applied. The boundary control is proportional to the angular velocity at the end. By spectral analysis, we prove that the optimal decay rate of the energy is given by the spectrum of the generator of the semigroup associated to the system.