This paper examines a coupled system of Kirchhoff-Carrier-type viscoelastic wave equations with Balarkrishnan-Taylor damping. The local existence and uniqueness of solutions for the given problem are proved by utilizing the Faedo-Galerkin method and linearization technique for nonlinear components. Additionally, by establishing sufficient conditions and constructing appropriate energy functionals, the energy of the solution generally decays as time approaches infinity.
Nam et al. (2025) studied this question.