Formula of Kirchhoff type for mixed problem

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