On the solution for a nonlinear wave equation with variable exponent nonlinearity and a varying delay.

This work examines a nonlinear wave equation characterized by a damping term whose exponent varies, along with a delay component that changes over time. The mathematical representation of the problem is provided below. [Formula: see text]To demonstrate the existence of global solutions, we impose suitable conditions on the functions [Formula: see text], [Formula: see text], ϖ and ϱ. This is achieved through the compactness method, specifically utilizing the Faedo-Galerkin approach. Furthermore, by applying the multiplier technique in conjunction with an integral inequality of Komornik type, we establish a quantitative assessment for how swiftly the system's energy diminishes over time.