Aissa Guesmia and Nasser-Eddine Tatar
Well-Posedness and Stability of a Retarded Impulsive Wave Equation with a Finite Memory
Dynamic Systems and Applications 32 (2023) 68-80

https://doi.org/10.46719/dsa2023.32.05

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 finite memory term. We prove the well-posedness and exponential stability of our system. Our stability result shows that the damping effect of the finite memory term is not destroyed neither by the impulses nor by the delay.

AMS (MOS) Subject Classification. 34B05, 34D05, 34H05.

Key Words and Phrases. Impulsive wave equation, Delay, Memory, Well-posedness,
Stability, Energy method, Differential inequalities.