Well-posedness and general decay of nonlinear coupled waves system with viscoelastic term

This research investigates a coupled wave system where the second equation is influenced by viscoelastic damping and is subject to Dirichlet boundary conditions on the interval (0, 1). For a broad class of relaxation functions and within a general framework, we establish the global existence of solutions using the Faedo-Galerkin method. In addition, we derive general decay estimates by applying Lyapunov?s method and employing certain convexity arguments.