THE DIRICHLET PROBLEM FOR A MIXED-TYPE EQUATION WITH TWO VARIABLE BOUNDARY CONDITIONS IN A RECTANGLE (Scientific journal of the Fergana State University, 2025)
The first boundary value problem for an elliptic-hyperbolic type equation with two internal perpendicular type change lines has been studied in a rectangular domain. The existence and uniqueness of the solution to the problem have been proven. The uniqueness of the solution was established using the completeness of the system of eigenfunctions in the corresponding space. The solution to the problem was constructed in the form of a series, leading to the issue of small denominators. It was shown that the denominator is nonzero.