EXPONENTIAL DECAY FOR A DELAYED DISPERSIVE-DISSIPATIVE WAVE EQUATION WITH TIME DEPENDENT COEFFICIENTS

We develop an alternative approach for treating discrete delay effects in wave equations. The proposed framework establishes exponential energy decay under the combined influence of structural damping and inertial dispersion. Unlike classical analyses, exponential stability is obtained without assuming that the instantaneous damping dominates the delayed feedback. The results reveal how delay and damping interact to generate stabilization mechanisms beyond previously known configurations. While our conditions are sufficient for exponential stability, determining the exact relationship among the delay, damping, and model coefficients remains an open problem.