Time decay of viscoelastic plates with type II heat conduction

Abstract

In this work, we consider the thermomechanical problem determined by a viscoelastic plate coupled with heat conduction of type II. This problem differs significantly from what can be found in the literature since we assume that the dissipation mechanism is mechanical while the heat conduction mechanism is conservative. We first prove the existence of a semigroup of contractions defining the solutions in a suitable Hilbert space. Exponential stability of the solutions is also proved by means of a known characterization of the exponentially stable semigroups. The lack of differentiability of the semigroup is also proved. Finally, we use energy arguments to show that the only solution that can be zero after a finite time is the null solution.