Regularity analysis for an abstract thermoelastic system with inertial term

In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations. The asymptotic stability of this model was investigated in [6]. We are able to decompose the parameter region into three parts where the semigroup associated with the system is analytic, of Gevrey class of specific order, and non-smoothing, respectively. Moreover, by a detailed and creative spectral analysis,, we will show that the order of Gevrey class is sharp, under proper conditions. We also show that the orders of the polynomial stability obtained in [6] is optimal.