Nonlocal Boundary-Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with Degeneration of Type and Order in the Hyperbolicity Domain

We consider a nonlocal boundary-value problem for a third-order parabolic-hyperbolic equation with degeneracy of type and order in the domain of hyperbolicity, containing second-order derivatives in the boundary conditions. Sufficient conditions of the unique solvability of the problem are obtained. The Tricomi method is used to prove the uniqueness theorem for a solution. The solution of the problem is expressed in the explicit form.