Boundary value problems with data on opposite characteristics for a second-order mixed-hyperbolic equation

In this paper, we study a nonlocal problem with a shift to conjugation of two equations of second-order hyperbolic type, consisting of a wave equation in one part of the domain and a degenerate hyperbolic equation of the first kind in the other part. Using the Tricomi method, sufficient conditions arc found for given functions that ensure the existence of a unique solution of the problem under study that is regular in the region under consideration. In a particular case, the solution of the problem is written out explicitly.