We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE's which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the
interior of a bounded domain Ω, coupled to a “parabolic–like”
beam equation holding on ∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave
equation via Neumann feedback control, and like that work, depends upon a
trace regularity estimate for solutions of hyperbolic equations.
