Exact controllability for a one-dimensional wave equation in non-cylindrical domains☆
Exact controllability for a one-dimensional wave equation in non-cylindrical domains☆
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DOI：
10.1016/j.jmaa.2013.01.062
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发表时间：
2013-06
影响因子：
1.3
通讯作者：
L. Cui;Xu Liu;Hang Gao
中科院分区：
文献类型：
--
作者：
L. Cui;Xu Liu;Hang Gao
本文致力于研究移动边界域中一维波动方程的可控性。该方程描述了一根具有固定端点和另一个移动端点的弦的运动。当运动端点的速度小于特征速度时，通过希尔伯特唯一性方法，该方程的精确可控性成立。此外，还给出了可控时间对移动端点速度的明确依赖性。此外，当移动端点的速度等于特征速度时，通过构造性方法，我们表征了平滑控制器精确可控性的目标集。
This paper is addressed to a study of the controllability for a one-dimensional wave equation in domains with moving boundary. This equation characterizes the motion of a string with a fixed endpoint and the other moving one. When the speed of the moving endpoint is less than the characteristic speed, by the Hilbert Uniqueness Method, the exact controllability of this equation is established. Also, an explicit dependence of the controllability time on the speed of the moving endpoint is given. Moreover, when the speed of the moving endpoint is equal to the characteristic speed, by a constructive method, we characterize a target set for the exact controllability with smooth controllers.