Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (6): 1461-1486.doi: 10.1007/s10473-019-0601-z

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DECAY ESTIMATE AND GLOBAL EXISTENCE OF SEMILINEAR THERMOELASTIC TIMOSHENKO SYSTEM WITH TWO DAMPING EFFECTS

Weike WANG1, Rui XUE2   

  1. 1. School of Mathematical Sciences & Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China;
    2. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2018-03-29 Revised:2019-04-02 Online:2019-12-25 Published:2019-12-30
  • Contact: Rui XUE,E-mail:xuemantian008@sjtu.edu.cn E-mail:xuemantian008@sjtu.edu.cn
  • Supported by:
    The first author is supported by National Natural Science Foundation of China (11771284).

Abstract: In this paper, we study a semilinear Timoshenko system with heat conduction having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one damping effect is rigorously proved here in providing optimality results. Moreover, the global well-posedness for small data is presented.

Key words: semilinear Timoshenko system, heat conduction, damping, optimal decay rate, eigenvalue expansion method

CLC Number: 

  • 35A01
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