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Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique

Published online by Cambridge University Press:  15 September 2002

Francis Conrad  and
Fatima-Zahra Saouri
Francis Conrad
Affiliation:
Institut Elie Cartan, Université de Nancy 1, BP. 239, 54506 Vandœuvre-lès-Nancy, France; [email protected].
Fatima-Zahra Saouri
Affiliation:
Institut Elie Cartan, Université de Nancy 1, BP. 239, 54506 Vandœuvre-lès-Nancy, France; [email protected].
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Abstract

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.

Keywords

Équation des poutrescontrôle frontièrestabilisation uniformeanalyse spectrale.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002 , pp. 567 - 595
Copyright
© EDP Sciences, SMAI, 2002

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