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Stabilization of second order evolution equations by a class of unbounded feedbacks

Published online by Cambridge University Press:  15 August 2002

Kais Ammari  and
Marius Tucsnak
Kais Ammari
Affiliation:
Institut Elie Cartan, Département de Mathématiques, Université de Nancy I, 54506 Vandœuvre-lès-Nancy Cedex, France
Marius Tucsnak
Affiliation:
Institut Elie Cartan, Département de Mathématiques, Université de Nancy I, 54506 Vandœuvre-lès-Nancy Cedex, France
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Abstract

In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

Keywords

Stabilizationobservability inequalitysecond order evolution equationsunbounded feedbacks.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 361 - 386
Copyright
© EDP Sciences, SMAI, 2001

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