Rivalry between a retarded term and a structural damping

We prove an exponential decay result for a wave equation with a strong damping competing with a time-retarded derivative of the state. This result covers cases that have not been previously considered in the literature and improves the existing ones. The focus will be on the relationship between the coefficients of these two terms. It is known that exponential stability occurs when the non-delayed damping term dominates the delayed one. In this work, we shed some light on what could happen if this condition is violated.