# Boundary controllability of structural acoustic systems with variable coefficients and curved walls

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## Abstract

This paper studies a structural acoustic model consisting of an interior acoustic wave equation with variable coefficients and a coupled Kirchhoff plate equation with a curved middle surface. By the Riemannian geometry approach and the multiplier technique, we establish exact controllability of the hybrid system under verifiable assumptions on the geometry of the interior domain and the interface boundary with two controls: One is a Neumann boundary control exerted on the wave equation, and the other acts on the interior of the plate equation. Furthermore, if the control for the plate equation is active alone, we prove that the hybrid system with partial Robin boundary condition of the wave equation is exactly controllable with the plate component and approximately controllable with the wave component.

## Keywords

Boundary controllability Structural acoustics model Variable coefficients Curved walls Riemannian geometry Multiplier method## Notes

### Acknowledgements

The authors would like to express their gratitude to the editors and reviewers for their valuable comments and helpful suggestions. This work is supported by National Natural Science Foundation (NNSF) of China under Grant Nos/ 61473126 and 61573342, and Key Research Program of Frontier Sciences, CAS, No. QYZDJ-SSW-SYS011, and Qatar National Research Funds Grant NPRP 9-166-1-031.

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