The initial-boundary value problem for the wave equation is considered in the three-dimensional half-space. The oscillation process is initiated by the initial data and the boundary mode. We prove a theorem of existence and uniqueness of the solution; it is presented in the form of the generalized Kirchhoff formula. This work can be considered as a generalization to the three-dimensional case of the classical result for equations of oscillations of a semi-bounded string.

中文翻译：

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混合问题的基尔霍夫型公式

在三维半空间中考虑波动方程的初边值问题。振荡过程由初始数据和边界模式启动。我们证明了解的存在唯一性定理；它以广义基尔霍夫公式的形式表示。这项工作可以被认为是对半有界弦振荡方程经典结果的三维情况的推广。