Well-posedness and stabilization of a type three layer beam system with Gurtin-Pipkin's thermal law

The goal of this work is to study the well-posedness and the asymptotic behavior of solutions of a triple beam system commonly known as the Rao-Nakra beam model. We consider the effect of Gurtin-Pipkin's thermal law on the outer layers of the beam system. Using standard semi -group theory for linear operators and the multiplier method, we establish the existence and uniqueness of weak global solution, as well as a stability result.