A Cauchy problem with initial data on difference surfaces for a system with singularity (Q1277437)

For the case where the initial data for different functions are given on different surfaces, we construct analytical solutions of a quasilinear partial differential equation system when the resulting problem has a concrete singularity of the form \(u/x\) or \(x/u\). The necessary and sufficient conditions for existence and uniqueness of the solution of this system in the form of formal power series are given as well as the sufficient condition for the convergence of these series. There is given a generalization of problems under consideration, which must be investigated in constructing the currents of ideal gas, which appear after a shock wave reflected by an axis or by a symmetry center.