Three-dimensional Initial-boundary Value Problem for a Parabolic-hyperbolic Equation With a Degenerate Parabolic Part

Initial-boundary value problem for a non-homogeneous equation of mixed parabolic-hyperbolic type in three variables with a degenerate parabolic part in a rectangular parallelepiped 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 of two natural arguments arises. Estimates on the separation of small denominators from zero with the corresponding asymptotics are established. These estimates made it possible to substantiate the convergence of the constructed series in the class of regular solutions of this equation. The stability of the solution with respect to the boundary function and the right-hand side of the equation is established.