Effects of history and heat models on the stability of thermoelastic Timoshenko systems (Q828286)

The Timoshenko system is a linear PDE system of two perturbed wave equations in dimension one. The two unknowns represent the vertical displacement and the rotation angle of a beam. In this paper the authors study a Timoshenko system with two damping mechanisms. A first damping term is a (nonlinear) history term given by an integral over time with an exponentially decaying kernel. A second damping mechanism is related to thermal effects: the system is complemented by a heat-like equation where the heat conduction is governed by a so-called Cattaneo law. The authors prove that the system is exponentially stable if the history term is present, while there is no exponential stability without history term.