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

George Avalos

Abstract and Applied Analysis, 1996, vol. 1, 1-15

Abstract:

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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:674967

DOI: 10.1155/S1085337596000103

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