A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations

In the cylindrical domain of Euclidean space for one class of multidimensional hyperbolic parabolic equations the spectral Dirichlet problem with homogeneous boundary conditions is considered. The solution is sought in the form of an expansion in multidimensional spherical functions. The existence and uniqueness theorems of the solution are proved. Conditions for the unique solvability of the problem are obtained, which essentially depend on the height of the cylinder