  In this paper, we provide a complete regularity analysis for an abstract
system of coupled hyperbolic and parabolic equations in a complex Hilbert
space. We are able to decompose the unit square of the parameters into three
parts where the semigroup associated with the system is analytic, of specific
order Gevrey classes, and non-smoothing, respectively. Moreover, we will show
that the orders of Gevrey class are sharp, under proper conditions.
