Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (2): 511-526.doi: 10.1016/S0252-9602(17)30018-8

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NONLINEAR ANALYSIS ON THE VIBRATION OF ELASTIC PLATES

Min DING, Shengbo GONG   

  1. 1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China;
    2. School of Mathematical Science and School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2016-03-14 Revised:2016-05-23 Online:2017-04-25 Published:2017-04-25
  • Supported by:

    Min Ding was supported in part by Innovation Award by Wuhan University of Technology under a project Grant 20410771; Shengbo Gong was supported in part by China Scholarship Council under Grant 201306230035.

Abstract:

We consider the vibration of elastic thin plates under certain reasonable assump-tions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the initial data, we establish the local time well-posedness for the initial and boundary value problem by Picard iteration scheme, and obtain the estimates for the solutions.

Key words: Vibration of elastic plates, Hamilton principle, well-posedness, Picard iteration

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