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Boundary controllability of a coupled wave/Kirchoff system

✍ Scribed by George Avalos; Irena Lasiecka; Richard Rebarber

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
289 KB
Volume
50
Category
Article
ISSN
0167-6911

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✦ Synopsis

We consider two problems in boundary controllability of coupled wave/Kircho systems. Let be a bounded region in R n , n ΒΏ 2, with Lipschitz continuous boundary . In the motivating structural acoustics application, represents an acoustic cavity. Let 0 be a at subset of which represents a exible wall of the cavity. Let z denote the acoustic velocity potential, which satisΓΏes a wave equation in , and let v denote the displacement on 0, which satisΓΏes a Kircho plate equation on 0. These equations are coupled via @z=@ = vt on 0 (where is the exterior unit normal to 0), and the backpressurezt appears in the Kircho equation. In the ΓΏrst problem, we consider a control u0 in the Kircho equation on 0, and an additional control u1 in the Neumann conditions on a subset 1 of , where \ 1 satisΓΏes geometric conditions. Using both controls, we obtain exact controllability of the wave and plate components in the natural state space. In the second problem we consider only the control u0. Without geometric conditions, exact controllability is not possible, but we show that for any initial data, we can steer the plate component exactly, and the wave component approximately.

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