Riemann problem for Born-Infeld systems

We consider the Born-Infeld system without differential constraints. Such a situation occurs as soon as the initial data don't satisfy the differential constraints. In this case, the Poynting vector is not a conservative variable and the technique of enlargement of systems cannot be applied. The resulting system consists of five conservative equations for which only one Riemann invariant exists. It is fully linearly degenerate but not strictly hyperbolic, nor is it rich. We prove that in (non-strictly) hyperbolic regions, the Riemann problem has a unique entropy solution for large initial data.