Local and nonlocal value boundary problems for a third-order mixed-type equation equipped with Tricomi operator in its hyperbolic part

The existence and uniqueness of local and nonlocal value boundary problems for third-order mixed-type equations with multiple characteristics is proved. Uniqueness of the problem solution is proved with energy-integral method. The existence of the solution is proved with equivalent reduction method to Fredholm integral equations of the second kind with the help of Green's function.