Three-dimensional Initial Boundary Value Problem for a Degenerate Equation of Mixed Parabolic-Hyperbolic Type

For an inhomogeneous equation of mixed parabolic-hyperbolic type with power degeneration in a rectangular parallelepiped, the initial boundary value problem is studied. A criterion for the uniqueness of a solution is established. The solution is constructed as the sum of an orthogonal series. When justifying the convergence of the series, the problem of small denominators from two natural arguments arose. Estimates are established for the separation of small denominators from zero with the corresponding asymptotic behavior. These estimates made it possible to substantiate the convergence of the constructed series in the class of regular solutions to this equation. The stability of the solution from the boundary function and the right side of the equation is established.