EXISTENCE THEORY FOR THE RIEMANN PROBLEM FOR NONCONSERVATIVE HYPERBOLIC SYSTEMS

In this Note, we study nonlinear and non-conservative hyperbolic syste ms in the framework introduced by Dal Maso-LeFloch-Murat. We prove an existence theorem of entropy weak solutions for the Riemann problem wh en the system is strictly hyperbolic, without assuming the genuine non linearity of the characteristic fields. We follow the new approach rec ently introduced by Tzavaras for the systems of conservation laws. Sel f-similar, smooth, approximate solutions are constructed, that are uni formly bounded in the BV norm and converge to a solution of the Rieman n problem. The structure of the elementary waves in this solution is s tudied, and we explain how to rigorously define the non-conservative p roducts.