Tricomi Problem for Mixed Parabolic–Hyperbolic Equation with Higher Order Boundary Condition.

In this paper, we study an analogue of Tricomi problem for a parabolic–hyperbolic equation. One boundary condition in the parabolic part of the domain contains the third derivative of the space variable. A spectral problem with a spectral parameter in the boundary condition arises, when solving this problem. The system of eigenfunctions of this problem (after removing any one eigenfunction) forms a Riesz basis. The conditions for the correctness of the formulated Tricomi problem are found. [ABSTRACT FROM AUTHOR]