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

Abstract

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.