Electron. J. Diff. Equ., Vol. 2011 (2011), No. 41, pp. 1-20.

Interior feedback stabilization of wave equations with time dependent delay

Serge Nicaise, Cristina Pignotti

We study the stabilization problem by interior damping of the wave equation with boundary or internal time-varying delay feedback in a bounded and smooth domain. By introducing suitable Lyapunov functionals exponential stability estimates are obtained if the delay effect is appropriately compensated by the internal damping.

Submitted July 26, 2010. Published March 17, 2011.
Math Subject Classifications: 35L05, 93D15.
Key Words: Wave equation; delay feedback; stabilization.

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Serge Nicaise
Université de Valenciennes et du Hainaut Cambrésis, MACS
ISTV, 59313 Valenciennes Cedex 9, France
email: serge.nicaise@univ-valenciennes.fr
Cristina Pignotti
Dipartimento di Matematica Pura e Applicata, Universitádi L'Aquila
Via Vetoio, Loc. Coppito, 67010 L'Aquila, Italy
email: pignotti@univaq.it

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