Exact boundary controllability of the structural acoustic model with variable coefficients

Abstract

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.

Keywords:

• Variable coefficients
• structural acoustic model
• exact controllability
• observability inequality
• Riemannian geometry theory

MSC Classifications:

• 35L55
• 93B05
• 93B07
• 93B27

Acknowledgments

The authors would like to express their gratitude to the editors and reviewers for their valuable comments and helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China under grant no. 11901329 and the Natural Science Foundation of Shandong Province of China under grant no. ZR2019BA022.