Stabilization of Second Order Evolution Equations with Unbounded Feedback with Time-Dependent Delay

der abstract second order evolution equations with unbounded feedback with time-varying delay. Existence results are obtained under some realistic assumptions. We prove the exponential decay under some ns by introducing an abstract Lyapunov functional. Our abstract framework is applied to the wave, to the beam and to the plate equations with boundary delays. Keywords second order evolution equations, wave equations, time-varying delay, stabilization, Lyapunov functional. AMS (MOS) subject classification 93D15, 93D05.

• Type: Journal
• Year: 2010
• Where: SIAMCO
• Authors: Emilia Fridman, Serge Nicaise, Julie Valein
• Keywords: Abstract Lyapunov, Order Evolution Equations, SIAMCO 2010, Time-varying Delay