Energy decay estimates for a two‐dimensional coupled wave‐plate system with localized frictional damping,ZAMM - Journal of Applied Mathematics and Mechanics

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Energy decay estimates for a two‐dimensional coupled wave‐plate system with localized frictional damping
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2019-11-24 , DOI: 10.1002/zamm.201900030
Ya‐Ping Guo ₁ , Jun‐Min Wang ₂ , Dong‐Xia Zhao ₃

Affiliation

This paper is devoted to the energy decay estimates for the two‐dimensional coupled wave‐plate system with local frictional damping in a bounded domain. The frictional damping is only distributed in the part of the plate's or wave's domain, and the other is stabilized by the transmission through the interface of the plate's and wave's domains. Using the frequency domain approach and the multiplier technique, we show respectively that the energy of the system decays polynomially under some geometric condition when the frictional damping only acts on the part of the plate, and the energy of the system is exponentially stable when the frictional damping acts only on the other part of the wave.

中文翻译：

具有局部摩擦阻尼的二维耦合波板系统的能量衰减估计

本文致力于有限域内具有局部摩擦阻尼的二维耦合波片系统的能量衰减估计。摩擦阻尼仅分布在板或波域的一部分中，而另一部分则通过通过板和波域的界面的传递来稳定。使用频域方法和乘数技术，我们分别表明，当摩擦阻尼仅作用于板的一部分时，系统的能量在某些几何条件下呈多项式衰减，当摩擦阻尼时系统的能量呈指数稳定。阻尼仅作用于波浪的另一部分。

更新日期：2019-11-24

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