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矩形区域热-板耦合系统的稳定性分析

余凯   

  1. 天津大学数学学院,天津  300354
  • 出版日期:2021-06-25 发布日期:2021-09-17

余凯. 矩形区域热-板耦合系统的稳定性分析[J]. 系统科学与数学, 2021, 41(6): 1481-1492.

YU Kai. Stability Analysis for Heat-Plate Interaction System on Rectangular Domain[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(6): 1481-1492.

Stability Analysis for Heat-Plate Interaction System on Rectangular Domain

YU Kai   

  1. School of Mathematics, Tianjin University, Tianjin 300354
  • Online:2021-06-25 Published:2021-09-17
该工作主要讨论在一二维矩形区域内的热-板耦合系统解的长时间行为. 该 模型由两部分组成: 其中一部分为热方程描述, 另一部分为欧拉-伯努利板方程描述. 两者在 公共边界处通过一定的传输条件耦合连接在一起. 基于频域分析方法, 结合正交分解以及 频域乘子构造等技巧, 得到了在光滑初始条件下该系统能量的多项式衰减速率估计.
This work is devoted to investigating the long time behavior of a heat-plate interaction system on a two-dimensional rectangular domain. The model consists of two parts: One is heat equation, and the other is Bernoulli-Euler plate equation, which are coupled through a common interface with certain transmission conditions. By applying the frequency domain method and separation of variables, we obtain the polynomial energy decay rate of the solution to this system under smooth initial conditions.
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