Mathematical models of Reissner-Mindlin thermoviscoelastic plates

We here investigate mathematical models describing deformations and thermal variations of a thin homogeneous thermoviscoelastic plate. First, a hereditary non-Fourier constitutive law for the heat flux and some heat power constitutive equation with linear memory are considered. Then, we adapt to hereditary relations some approximation procedures previously established for thermoelastic plates and due to Lagnese and Lions. The resulting models are derived in the framework of the well-established theory of heat conduction, thanks to Gurtin and Pipkin, and according to the standard approximation procedure for the Reissner-Mindlin plate model.