Publication ahead of print Issue ESAIM: COCV DOI 10.1051/cocv/2009007 Published online 21 April 2009

ESAIM: COCV
DOI: 10.1051/cocv/2009007

Stabilization of second order evolution equations with unbounded feedback with delay

Serge Nicaise and Julie Valein

Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, 59313 Valenciennes Cedex 9, France. Serge.Nicaise@univ-valenciennes.fr; Julie.Valein@univ-valenciennes.fr

Received April 16, 2008. Revised September 19, 2008 and December 1st, 2008. Published online April 21, 2009.

Abstract
We consider abstract second order evolution equations with unbounded feedback with delay. Existence results are obtained under some realistic assumptions. Sufficient and explicit conditions are derived that guarantee the exponential or polynomial stability. Some new examples that enter into our abstract framework are presented.

Mathematics Subject Classification. 93D15, 93C20

Key words: Second order evolution equations, wave equations, delay, stabilization functional


© EDP Sciences, SMAI 2009

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