  n this work we consider a multilayered heat-wave system where a 3-D heat
equation is coupled with a 3-D wave equation via a 2-D interface whose dynamics
is described by a 2-D wave equation. This system can be viewed as a
simplification of a certain fluid-structure interaction (FSI) PDE model where
the structure is of composite-type; namely it consists of a \textquotedblleft
thin\textquotedblright\ layer and a \textquotedblleft thick\textquotedblright\
layer. We associate the wellposedness of the system with a strongly continuous
semigroup and establish its asymptotic decay.
  Our first result is semigroup well-posedness for the (FSI) PDE dynamics.
Utilizing here a Lumer-Phillips approach, we show that the fluid-structure
system generates a $C_0$-semigroup on a chosen finite energy space of data. As
our second result, we prove that the solution to the (FSI) dynamics generated
by the $C_0$-semigroup tends asymptotically to the zero state for all initial
data. That is, the semigroup of the (FSI) system is strongly stable. For this
stability work, we analyze the spectrum of the generator $\mathbf A$ and show
that the spectrum of $\mathbf A$ does not intersect the imaginary axis.
\vskip.3cm \noindent \textbf{Key terms:} Fluid-structure interaction, heat-wave
system, well-posedness, semigroup, strong stability.
