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

George Avalos

Abstract and Applied Analysis, 1996, vol. 1, issue 2, 203-217

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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https://doi.org/10.1155/S1085337596000103

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:1:y:1996:i:2:p:203-217

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