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

Abstract

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. Additionally, we derive general decay estimates by  applying Lyapunov’s method  and employing certain convexity arguments.