Acta mathematica scientia,Series A ›› 2024, Vol. 44 ›› Issue (4): 946-959.

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Stabilization of 2-D Mindlin Timoshenko Plate Systems with Local Damping

Zhang Chunguo1,*(),Sun Baonan1,Fu Yuzhi1,Yu Xin2   

  1. 1Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018
    2School of Computer and Data Engineering, Ningbo Tech University, Zhejiang Ningbo 315100
  • Received:2023-04-29 Revised:2023-10-07 Online:2024-08-26 Published:2024-07-26
  • Supported by:
    NSFC(61503103);key project of Zhejiang Provencial Natural Science Foundation(LZ21A010001)

Abstract:

In this paper, the two-dimensional Mindlin-Timoshenko plate system with local damping is studied. First, the original system is transformed into an abstract Cauchy problem, and the well posedness of the system is obtained by using operator semigroup theory. With the help of the frequency domain stability results of the linear system, the uniform exponential stability of the system is obtained by introducing geometric optical conditions and multiplier techniques.

Key words: Mindlin-Timoshenko plate system, Local damping, Piecewise multiplier method, Uniform exponential stability.

CLC Number: 

  • O231.4
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