LAUSR

We study an initial–boundary value problem for an equation of the mixed parabolic-hyperbolic type in a rectangular parallelepiped. A uniqueness criterion is established. The solution is constructed in the form of a series in an orthogonal function system. The problem of small denominators depending on two positive integer arguments arises when justifying the convergence of this series. Sufficient conditions are found for the uniform separation of the denominators from zero; this permits us to prove the convergence of the series in the class of regular solutions and the stability of the solution with respect to perturbations of the boundary functions.