Admissible Riemann Solvers for Genuinely Nonlinear p-Systems of Mixed Type

We consider in this paper the Riemann problem for p-systems of mixed type that define two hyperbolic phases with a stress function satisfying general genuinely nonlinear hypotheses. We describe here all the global Riemann solvers that are continuous for the L¹ distance with respect to initial data while conserving the natural symmetry properties of the p-system and coinciding with the Lax solution when defined: these Riemann solvers can be described entirely by a kinetic function, used to select a manifold of subsonic phase transitions and a corresponding set of supersonic phase transitions.