On a non-local problem for mixed parabolic-hyperbolic type equation with non-smooth line of type changing

In the present article we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic type equation with three lines of type changing. Considered mixed domain contains a rectangle as a parabolic part and three domains bounded by smooth curves and by type-changing lines as a hyperbolic part of the mixed domain. We prove the uniqueness applying energy integral method. The proof of the existence will be done by reducing the original problem into the system of the second kind Volterra integral equations.