The Riemann problem for a simple model of phase transition

We consider in this paper a simple model of liquid-vapor phase transition. The PDE system corresponds to the isothermal p-system and the pressure law is defined for all positive density and involves a constant zone. Such a pressure law can occur for instance when considering the Van der Waals equation of state complemented by the Maxwell's law. The Riemann problem is globally solved for all initial states, as well in the pure phases as in the mixture zone.