Blowing-up solutions for the Moorea-Gibson-Thompson equation with a viscoelastic memory and an external force

The Moore-Gibson-Thompson equation with a viscoelastic memory and a forcing term is considered. The existence and uniqueness of a local solution are obtained via Faedo-Galerkin's method. Furthermore, it is shown that solutions with or without a positive initial energy experience blowing-up due to the nonlinear forcing term.