Boundary Value Problems for a Third Order Mixed Parabolic-hyperbolic Equation with Variable Coefficients

The existence and uniqueness of a solution to the boundary value problem for a third-order parabolic-hyperbolic equation with variable coefficients in the lower terms is proved. Using method for reducing the order of an equation, the problem is reduced to the Tricomi problem for a parabolic-hyperbolic type equation of second order. The solvability of the problem is reduced to the solvability of the Fredholm integral equation of the second kind. After determining the trace of a function and its first-order derivatives with respect to \(y\) , the solution to the problem is completely determined in the regions under consideration.