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.