This article focuses on the exact null controllability of a one-dimensional wave equation in noncylindrical domains. Both the fixed endpoint and the moving endpoint are Neumann-type boundary conditions. The control is put on the moving endpoint. When the speed of the moving endpoint is less than the characteristic speed, we can obtain the exact null controllability of this equation by using the Hilbert uniqueness method. In addition, we get a sharper estimate on controllability time that depends on the speed of the moving endpoint.

中文翻译：

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具有诺伊曼边界的弦方程的精确空可控性

本文重点研究非圆柱域中一维波动方程的精确零可控性。固定端点和移动端点均为诺伊曼型边界条件。控制权放在移动端点上。当运动端点的速度小于特征速度时，利用希尔伯特唯一性方法可以得到该方程的精确零可控性。此外，我们还可以更准确地估计可控时间，这取决于移动端点的速度。