Abstract and Applied Analysis · 1996 · 66 citations · 9 references
Natural SciencesMechanical EngineeringPhysicsAcousticsDynamical SystemsFluid DynamicsAcoustic Wave PropagationAeroacousticsHyperbolic DynamicsPhysical AcousticsStructural AcousticsWave Propagation In StructuresAcoustic Wave EquationsAcoustic-structure InteractionCoupled Acoustic-structural InteractionCoupled Fluid-structure InteractionExponential StabilityFeedback Control TheoryFluid-structure-acoustic InteractionStabilization
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.
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