具有点反馈的Rayleigh梁的能量衰减估计

摘要

本文研究在某种边界条件下具有点反馈的Rayleigh梁的能量衰减估计.证明了梁的能量一致指数衰减是不可能发生的.在能量空问中,当梁的能量非一致衰减时,由初始条件得到了梁的能量多项式衰减估计.本文的方法是由相应无阻尼系统产生观测不等式和迹正则性结果得到的衰减估计.%In this paper, we study the energy decay estimate of the Rayleigh beam which is subject to a pointwise feedback with certain boundary conditions, we show that the uniform energy decay may not occur. In the case of nonuniform decay in the energy space, we derive explicit polynomial decay estimates valid for regular initial data. Our method consists of deducing the decay estimates from observability inequalities for associated undamped problem via sharp trace regularity results.