A three-dimensional analog of the Tricomi problem for a parabolic-hyperbolic equation

For a parabolic-hyperbolic equation, we study the three-dimensional analog of the Tricomi problem with a noncharacteritic plane on which the type of the equation changes. The uniqueness of the solution to the problem is proved by the method of a priori estimates, and the existence of a solution is reduced to the existence of a solution to a Volterra integral equation of the second kind.