Abstract The aim of this paper is to prove the averaged null controllability property for a wave equation with an unknown velocity of propagation parameter and for parameter-dependent vibrating plate equation under the effect of a boundary control. The choice of the Hilbert uniqueness method seems to be the best-adapted method to our theory, where the key point to prove the desired result is an averaged inverse inequality (averaged observability inequality). Consequently, we'll prove the desired property for a large time enough and we'll design a single control chosen independently of the parameter value transferring the average of the state to the origin.

中文翻译：

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某些双曲方程的平均零可控性取决于参数

摘要 本文的目的是证明具有未知传播速度参数的波动方程和边界控制作用下的参数相关振动板方程的平均零位可控性。希尔伯特唯一性方法的选择似乎是最适合我们理论的方法，其中证明所需结果的关键点是平均逆不等式（平均可观察性不等式）。因此，我们将在足够长的时间内证明所需的属性，并且我们将设计一个独立于将状态平均值传输到原点的参数值选择的单个控件。