Two problems for three-dimensional space analogue of the third order hyperbolic type equation

For a complete hyperbolic equation of the third order with variable coefficients in the infinite rectangle the problem with two integral conditions and conjugation on the characteristic plane (Problem I) is considered. As auxiliary Darboux problem is solved by Riemann method which is much simplified by the special presentation of one of the boundary conditions. Taking Darboux problem as a basis for the solution, authors reduce the Problem I to the uniquely solvable integral equation, which gives an explicit solution to the Problem I.