Existence and stability for some strongly damped wave equations in the presence of strong delay

In this project, we consider some wave equations in the presence of strong damping and internal and distributed strong delays and discuss the existence and stability. In the absence of the delay, this type of equations has been extensively studied in the literature and many existence, nonexistence and stability results have been established. Introducing a delay term makes the problem different from those considered in the literature since even a weak delay may be a source of instability as shown in many cases. Our goal here is to investigate the effect of the delay and determine necessary and/or sufficient conditions for obtaining uniform stability.