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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 theinterior 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 waveequation via Neumann feedback control, and like that work, depends upon atrace regularity estimate for solutions of hyperbolic equations

The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics