论文标题
洛伦兹压电束具有部分粘性阻尼的稳定结果
Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings
论文作者
论文摘要
在本文中，我们研究了具有部分粘性阻尼的一维洛伦兹压电（拉伸系统）的稳定。首先，通过使用洛伦兹仪条件，我们重新制定了系统以实现解决方案的存在和独特性。接下来，通过使用Arendt-Batty的一般标准，我们证明了不同情况下的稳定性。最后，我们证明，在x方向上控制梁的中心线的伸展足以达到指数稳定性。还提出了数值结果以验证我们的理论结果。
In this paper, we investigate the stabilization of a one-dimensional Lorenz piezoelectric (Stretching system) with partial viscous dampings. First, by using Lorenz gauge conditions, we reformulate our system to achieve the existence and uniqueness of the solution. Next, by using General criteria of Arendt-Batty, we prove the strong stability in different cases. Finally, we prove that it is sufficient to control the stretching of the center-line of the beam in x-direction to achieve the exponential stability. Numerical results are also presented to validate our theoretical result.
