  We consider a multilayer hyperbolic-parabolic PDE system which constitutes a
coupling of 3D thermal - 2D elastic - 3D elastic dynamics, in which the
boundary interface coupling between 3D fluid and 3D structure is realized via a
2D elastic equation. Our main result here is one of strong decay for the given
multilayered - heat system. That is, the solution to this composite PDE system
is stabilized asymptotically to the zero state.
  Our proof of strong stability takes place in the "frequency domain" and
ultimately appeals to the pointwise resolvent condition introduced by Tomilov
[45]. This very useful result, however, requires that the semigroup associated
with our multilayered FSI system be completely non-unitary (c.n.u).
Accordingly, we firstly establish that the semigroup $\{e^{\mathcal
{A}t}\}_{t\geq 0}$ is indeed c.n.u., in part by invoking relatively recent
results of global uniqueness for overdetermined Lam\'e systems on nonsmooth
domains. Although the entire proof also requires higher regularity results for
some trace terms, this \textit{"resolvent criterion approach"} allows us to
establish a "classially soft" proof of strong decay. In particular, it avoids
the sort of technical PDE multipliers invoked in [9].
