Classical Solution of the First Mixed Problem for the WaveEquation in Cylindrical Domain in Odd-Dimensional Space

The classical solution of the first mixed problem for the wave equation in the cylindrical area in an odd-dimensional space is considered. The solution is constructed using spherical averaging operators which allow the reduction of the equation to the first mixed problem for the one-dimensional wave equation. Using the method of characteristics the explicit solution is obtained and necessary and sufficient matching conditions for the existence of a unique classical solution are proved.