Riemann Problems and Exact Solutions for the p-System

In this paper, within the framework of Method Differential Constraints, celebrated p-system is studied. All possible constraints compatible with original governing system are classified. solving compatibility conditions between and appended differential constraint, several model laws for pressure p(v) characterised. Therefore, analysis developed in paper has been carried out case physical interest where p=p0v−γ, an exact solution that generalises simple waves determined. This allows us to study solve a class generalised Riemann problems (GRP). particular, we proved GRP can be discussed (p,v) plane through rarefaction-like curves shock curves. Finally, studied problem structure existence critical time after which solved terms non-constant states separated by wave wave.