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Uniform Decay Rates for a Variable-Coefficient Structural Acoustic Model with Curved Interface on a Shallow Shell

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Abstract

Uniform stabilization of a structural acoustic model describing an acoustic chamber with flexible curved wall is addressed. The coupled nonlinear system consists of a variable-coefficient wave equation and a shallow shell model which is used to model the flexible curved wall (interface). The coupling between the wave and the shell takes place on the interface. Derivation of stability estimates for the variable-coefficient coupled system with the shallow shell depends on the Riemannian geometry method and the multiplier technique. The uniform energy decay rates of the overall interactive model are achieved by introducing nonlinear boundary feedbacks applied to the wave equation and the shell model.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, Shanxi, China

    Jing Li & Shugen Chai

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  1. Jing Li
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  2. Shugen Chai
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Correspondence to Jing Li.

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This work is supported by National Nature Science Foundation of China for the Youth (11801339), National Natural Science Foundation of China (62273217,12131008), Nature Science Foundation of Shanxi Province (201901D111042, 201901D211162), Shanxi Scholarship Council of China (2020-006).

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Li, J., Chai, S. Uniform Decay Rates for a Variable-Coefficient Structural Acoustic Model with Curved Interface on a Shallow Shell. Appl Math Optim 87, 56 (2023). https://doi.org/10.1007/s00245-023-09968-2

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