Well-Posedness and Stability of a Retarded Impulsive Wave Equation with a Finite Memory

Abstract

. Of concern is a wave equation which takes into account a discrete time delay in the state itself (and not in its time derivative). It is also subject to impulses and a control given by a (cid:12)nite memory term. We prove the well-posedness and exponential stability of our system. Our stability result shows that the damping effect of the (cid:12)nite memory term is not destroyed neither by the impulses nor by the delay.