In this paper, we study one‐dimensional linear degenerate wave equations with a distributed controller. We establish observability inequalities for degenerate wave equation by multiplier method. We also deduce the exact controllability for degenerate wave equation by Hilbert uniqueness method when the control acts on the nondegenerate boundary. Moreover, an explicit expression for the controllability time is given.

中文翻译：

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某些简并波动方程的精确可控性

在本文中，我们使用分布控制器研究一维线性简并波动方程。我们用乘数法建立了简并波动方程的可观测性不等式。当控制作用于非退化边界时，我们还采用希尔伯特唯一性方法推导了退化波动方程的精确可控性。此外，给出了可控制时间的明确表达式。