On the analyticity of the MGT-viscoelastic plate with heat conduction

Abstract

We consider a viscoelastic plate equation of Moore-Gibson-Thompson type coupled with two different kinds of thermal laws, namely, the usual Fourier one and the heat conduction law of type III. In both cases, the resulting system is shown to generate a contraction semigroup of solutions on a suitable Hilbert space. Then we prove that these semigroups are analytic, despite the fact that the semigroup generated by the mechanical equation alone does not share the same property. This means that the coupling with the heat equation produces a regularizing effect on the dynamics, implying in particular the impossibility of the localization of solutions. As a byproduct of our main result, the exponential stability of the semigroups is established.