The generalized problem of breakup of an arbitrary discontinuity (Q1190073)

The problem of breakup of an arbitrary discontinuity in a gas (the Riemann problem) is generalized to the case when an arbitrary, in general space-variable, distribution of the gas-dynamic parameters is given on both sides of the discontinuity at the initial instant of time (the generalized Riemann problem). The solvability of this, in general non- selfsimilar model is proved and analytical formulas are found for its solution in a small neighbourhood of the points of discontinuit in the \(x\), \(t\) plane, where \(x\) is the space coordinate and \(t\) is the time.