To Investigation of The Mixed Problem For Systems of Equations of Compound Type

 The article is devoted to the solvability of the mixed problem of a system of two second-order partial differential equations of composite type (hyperbolic-elliptic type). In contrast to previous studies for bounded in, for solving the mixed problem, an initial condition is given in a new setting. It should be noted that in previous studies in the mixed problem, the initial conditions were specified as two separate (separate hyperbolic and separate elliptic) equations. Solutions to various problems are obtained in the form of series, and the absolute and uniform convergence of these series, as well as the series obtained from these series by differentiation with respect to and up to two times, is proved