CLASSICAL SOLUTION OF THE FIRST MIXED PROBLEM FOR THE WAVE EQUATION IN CYLINDRICAL DOMAIN IN ODD DIMENSIONAL SPACE

The classical solution of the first mixed problem for the wave equation in the cylindrical area in the space with odd number of dimensions is considered. The solution is constructed using the spherical averages operators which allows the reduction of the equation to the first mixed problem for the one-dimensional wave equation. Using the characteristics method the explicit solution is obtained and necessary and sufficient matching conditions for the existance of the unique classical solution are proved.