Exact boundary controllability of the structural acoustic model with variable coefficients

We consider the boundary controllability of the structural acoustic model with variable coefficients. The structural acoustic model is a coupled partial differential equation, which comprises an acoustic wave equation in the interior domain, a Kirchoff plate equation on the boundary portion, with th...

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Bibliographic Details
Published inApplicable analysis Vol. 102; no. 9; pp. 2524 - 2539
Main Author Liu, Yu-Xiang
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 13.06.2023
Taylor & Francis Ltd
Subjects
Acoustic waves
Controllability
exact controllability
Mathematical models
observability inequality
Partial differential equations
Plate material
Riemannian geometry theory
structural acoustic model
Variable coefficients
Wave equations
Wave propagation
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ISSN0003-6811
1563-504X
DOI10.1080/00036811.2022.2030722

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Summary:We consider the boundary controllability of the structural acoustic model with variable coefficients. The structural acoustic model is a coupled partial differential equation, which comprises an acoustic wave equation in the interior domain, a Kirchoff plate equation on the boundary portion, with the coupling being accomplished across a boundary interface. In this model, the wave propagation medium and the plate material are all inhomogeneous. By the Riemannian geometry theory and the multiplier technique, our paper derives the exact controllability with two boundary controls under some checkable conditions and the exact-approximate boundary reachability with only one control for the boundary Kirchoff plate equation.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2022.2030722