Application of the generalized method of characteristic series to the construction of a solution of an initial-boundary value problem for a system of quasi-linear equations

A generalization of the method of characteristic series developed by A. F. Sidorov is suggested. The method is applied to the investigation of initial-boundary value problems for partial differential equations, including equations appearing in gas dynamics. A solution of a mixed problem for a system of quasi-linear equations is constructed in the form of multiple series in powers of characteristic functions, and the corresponding analog of the Cauchy–Kovalevskaya theorem is proved.