Well-posedness and stability analysis for Timoshenko beam system with Coleman-Gurtin's and Gurtin-Pipkin's thermal laws

In this article, the effect of Coleman-Gurtin's and Gurtin-Pipkin's thermal laws on the displacement of a Timoshenko beam system with suspenders is studied. Using the existing semi-group theory and energy method, the existence and uniqueness of weak global solution, as well as a stability result without imposing any conditions on the coefficient parameters, are established.