Remark on stabilization of second order evolution equations by unbounded dynamic feedbacks and applications

Zainab Abbas (1) , Kais Ammari (2) , Denis Mercier (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 FSM - Faculté des Sciences de Monastir

In this paper we consider second order evolution equations with unbounded dynamic 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.

Mots clés: Unbounded Dynamic feedback; Observability; Uniform stability; Non uniform stability.; Non uniform stability

Domaines: Equations aux dérivées partielles [math.AP]

Zainab Abbas, Kais Ammari, Denis Mercier. Remark on stabilization of second order evolution equations by unbounded dynamic feedbacks and applications. 2014. ⟨hal-01022854⟩