Analysis of configurations arising in the decay of an arbitrary discontinuity

The classical problem in mechanics of the decay of an arbitrary discontinuity is important for computational mathematics as an element of Godunov's finite-difference method. This paper examines the first part of the problem, i.e., the determination of the type of decay in the case of the equations of state of real media. A new approach to the analysis of types of decay configurations is presented; it involves the determination of the sign of four functions, two of which are found precisely, while two are found approximately.