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Stability of Transmission Wave-Plate Equations with Local Indirect Damping

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Abstract

This paper is devoted to the energy decay estimates for the coupled wave-plate system with local frictional damping in a bounded domain. The frictional damping distributes in the plate or wave domain. When the frictional damping is only acting through the plate equation, the transmission system is showed not to be exponentially stable. By the frequency domain approach and multiplier technique, it is found that the system energy has the polynomial decay rate. On the other hand, when the frictional damping only act through the wave equation, it is showed that the system energy has the exponential decay. It can be seen that only the frictional damper acting on the wave equation can stabilize exponentially the transmission plate-wave equations.

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Authors and Affiliations

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

    Ya-Ping Guo

  2. School of Mathematics and Statistics, Key Laboratory of Mathematical Theory and Computation in Information Security, Beijing Institute of Technology, Beijing, China

    Jun-Min Wang

  3. Department of Mathematics, North University of China, Taiyuan, China

    Dong-Xia Zhao

Authors
  1. Ya-Ping Guo
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  2. Jun-Min Wang
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  3. Dong-Xia Zhao
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Correspondence to Jun-Min Wang.

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This work was supported by the National Natural Science Foundation of China (No. 62073037 and No. 11871315) and the Natural Science Foundation (NSF) of Shanxi Province for the Youth (No. 201901D211162).

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Guo, YP., Wang, JM. & Zhao, DX. Stability of Transmission Wave-Plate Equations with Local Indirect Damping. Acta Appl Math 177, 10 (2022). https://doi.org/10.1007/s10440-022-00471-4

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  • DOI: https://doi.org/10.1007/s10440-022-00471-4

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