Advances in Differential Equations

Exact controllability of finite energy states for an acoustic wave/plate interaction under the influence of boundary and localized controls

George Avalos and Irena Lasiecka

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Abstract

In this work, we derive a result of exact controllability for a structural acoustic partial differential equation (PDE) model, comprised of a three-dimensional interior acoustic wave equation coupled to a two-dimensional Kirchoff plate equation, with the coupling being accomplished across a boundary interface. For this PDE system, we show that by means of boundary controls, the interior wave and Kirchoff plate initial data can be steered to an arbitrary finite energy state. In this work, key use is made of recent, microlocally-derived, $L^{2}\times H^{-1}$ "recovery" estimates for wave equations with Dirichlet boundary data. Moreover, the coupling of the disparate acoustic wave/Kirchoff plate dynamics is reconciled by means of sharp regularity estimates which are valid for hyperbolic equations of second order.

Article information

Source
Adv. Differential Equations Volume 10, Number 8 (2005), 901-930.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867823

Mathematical Reviews number (MathSciNet)
MR2150870

Zentralblatt MATH identifier
1100.60504

Subjects
Primary: 93B05: Controllability
Secondary: 35L05: Wave equation 74K20: Plates 74M05: Control, switches and devices ("smart materials") [See also 93Cxx] 76Q05: Hydro- and aero-acoustics

Citation

Avalos, George; Lasiecka, Irena. Exact controllability of finite energy states for an acoustic wave/plate interaction under the influence of boundary and localized controls. Adv. Differential Equations 10 (2005), no. 8, 901--930. https://projecteuclid.org/euclid.ade/1355867823.


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