论文标题
轴向行进的绳子的能量衰减估计在一端阻尼
Energy decay estimates for an axially travelling string damped at one end
论文作者
论文摘要
我们研究轴向行进的绳子的小振动，并在一端进行仪表板阻尼。该字符串由波动方程建模，以时间相关的间隔为间隔，两个端点以恒定速度$ v $移动。对于未阻尼的情况，我们获得了与溶液能量相同的保守功能。我们得出了具有显式常数的能量指数衰减的精确估计值。即使对于非旅行案例$ v = 0 $，这些估计似乎也没有在文献中报告。
We study the small vibrations of an axially travelling string with a dashpoint damping at one end. The string is modelled by a wave equation in a time-dependent interval with two endpoints moving at a constant speed $v$. For the undamped case, we obtain a conserved functional equivalent to the energy of the solution. We derive precise upper and lower estimates for the exponential decay of the energy with explicit constants. These estimates do not seem to be reported in the literature even for the non-travelling case $v=0$.
