  In this work, we consider a certain multilayered (thick layer) wave--(thin
layer) wave--heat (fluid) interactive PDE system. Such coupled PDE systems have
been used in the literature to describe the blood transport process in
mammalian vascular systems. In particular, the deformations of the boundary
interface (thin layer) are described via the two dimensional elastic equation.
The present work constitutes an investigation of the extent of the stabilizing
effects of the underlying fluid dissipation -- across the boundary interface --
upon both the thick and thin structural components. (All three PDE components
evolve on their respective geometries.) In this regard, our main result is the
derivation of uniform decay rates for classical solutions of this multilayered
PDE model. To obtain these estimates, necessary a priori inequalities for
certain static multilayered PDE models are generated here to ultimately allow
an application of a wellknown resolvent criterion for rational decay.
