General decay for a coupled wave problem with Lord-Shulman thermal heat law and delay

This article study a coupled one-dimensional hyperbolic system with Lord-Shulman thermal heat law on the first equation, and a general weak inherent damping, along with time-dependent coefficient and time-varying delay term on the second equation. Using the multiplier method, through a suitable Lyapunov functional, we prove a general decay stability result that encompasses both exponential and polynomial decay estimates as special cases. This result extends and generalizes existing findings in the literature related to the system under study.