Exact Controllability and Stabilization of a Vibrating String with an Interior Point Mass
Exact Controllability and Stabilization of a Vibrating String with an Interior Point Mass
复制标题
具有内点质量的振动弦的精确可控性和稳定性
DOI：
--
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
E. Zuazua
中科院分区：
文献类型：
--
作者：
S. Hansen;E. Zuazua
在本文中，我们研究具有内点质量的一维波动方程的边界控制和稳定问题。我们证明，波中的奇点在穿过质量点时会被“平滑一阶”。因此，在一个内点质量的情况下，例如，在左端使用 $L^2$-Dirichlet 控制，可以预期的最一般的可达空间（从 0 开始）是质量左侧的 $L^2 imes H^{-1}$ 和质量右侧的 $H^1 imes L^2$。我们证明这实际上是最佳结果（以某些兼容性条件为模）。还给出了此类系统的控制和稳定的一些相关结果。
In this article we examine the problems of boundary control and stabilization for a one-dimensional wave equation with interior point masses. We show that singularities in waves are "smoothed one order" as they cross a point mass. Thus in the case of one interior point mass, with, e.g., $L^2$-Dirichlet control at the left end, the most general reachable space (from 0) that one can expect is $L^2 imes H^{-1}$ to the left of the mass and $H^1 imes L^2$ to the right of the mass. We show that this is in fact the optimal result (modulo certain compatibility conditions). Several related results for both control and stabilization of such systems are also given.