论文标题
一些LQ（r） - 鼻衰减估计值的两个cauchy类型的rao-nakra三明治梁具有摩擦阻尼或无限记忆
Some Lq(R)-norm decay estimates for two Cauchy systems of type Rao-Nakra sandwich beam with a frictional damping or an infinite memory
论文作者
论文摘要
在本文中，我们考虑了整个线R中的两种类型的Rao-Nakra夹层梁，具有摩擦阻尼或作用在Euler-Bernoulli方程式上的无限记忆。当两个波方程的传播速度相等时，我们表明，当时间到达无穷大时，解决方案不会收敛到零。在相反的情况下，我们证明了一些L2（r） - 纳米和L1（R） - 纳米衰减估计及其高阶衍生物相对于空间变量的估计。由于插值不平等和卡尔森不等式，对于任何Q> 1，这些L2（r） - 纳米和L1（R） - 衰变估计值在LQ（R） - norm中导致相似的估计值。在我们的L2（r） - 纳米和L1（R） - 纳米衰减估计值中，我们根据初始数据的规律性和控制性质指定衰减率。
In this paper, we consider two systems of type Rao-Nakra sandwich beam in the whole line R with a frictional damping or an infinite memory acting on the Euler-Bernoulli equation. When the speeds of propagation of the two wave equations are equal, we show that the solutions do not converge to zero when time goes to infinity. In the reverse situation, we prove some L2(R)-norm and L1(R)-norm decay estimates of solutions and theirs higher order derivatives with respect to the space variable. Thanks to interpolation inequalities and Carlson inequality, these L2(R)-norm and L1(R)-norm decay estimates lead to similar ones in the Lq(R)-norm, for any q>1. In our both L2(R)-norm and L1(R)-norm decay estimates, we specify the decay rates in terms of the regularity of the initial data and the nature of the control.
