The third boundary problem for the hyperbolic differential equation of the second order

Abstract

This article consider the solvability of the problem for the model linear homogeneous differential equation with partial derivatives of the second order of hyperbolic type on the plane in the square for the case of discontinuous conjugation conditions on the characteristics with the third series boundary conditions on the whole boundary of the region under consideration. Dalamber’s solution is used for this problem solving. The conditions for the single-valued solvability of the defined problem are clarified in this paper. As a result, an exact solution was obtained in an explicit form.