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Stabilization of 2-d Mindlin-Timoshenko plates with localized acoustic boundary feedback

  • * Corresponding author: Chunguo Zhang, Tehuan Chen

    * Corresponding author: Chunguo Zhang, Tehuan Chen 

This research was supported by the National Key R & D Program of China (No. 2019YFB1705800), the National Natural Science Foundation of China under (No. 61973270), the Fundamental Research Funds for the Central Universities of China (No. 2018XZZX001-09) and Zhejiang Provincial Natural Science Foundation of China (No. LY21F030003)

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  • In this paper, we investigate the well-posedness and the asymptotic stability of a two dimensional Mindlin-Timoshenko plate imposed the so-called acoustic control by a part of the boundary and a Dirichlet boundary condition on the remainder. We first establish the well-posedness results of our model based on the theory of linear operator semigroup and then prove that the system is not exponentially stable by using the frequency domain approach. Finally, we show that the system is polynomially stable with the aid of the exponential or polynomial stability of a system with standard damping acting on a part of the boundary.

    Mathematics Subject Classification: Primary: 35B40, 93D15, 93D20.


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