ON BOUNDARY TASKS FOR THE EQUATION MIXED PARABOLIC-HYPERBOLIC TYPE OF THE THIRD ORDER WITH MINOR TERMS

Abstract

The existence and uniqueness of a solution to a boundary value problem for an equation of a mixed parabalo-hyperbolic type of the third order with variable coefficients at lower terms is proved. A feature of this problem is that the mixed parabolic-hyperbolic operator is applied to an ordinary differential operator with respect to the variable x. By the order reduction method, the problem under consideration is reduced to the Goursat problem for a hyperbolic type equation in a characteristic triangle and to the first boundary value problem for a parabolic type equation in a rectangle. The solvability of the problem is reduced to the solvability of the Fredholm integral equations of the second kind. After determining the trace of the function and its derivative with respect to y, the solution of the problem is completely determined in the areas under consideration.