On a $2x2$ system of conservation laws with discontinuous flux

We study a one-dimensional $2x2$ system of conservation laws with discontinuous flux. We prove the global existence of weak solutions for initial data with sufficiently small total variation. We construct explicitly the associated Riemann solver and analyze its main properties. Finally, we introduce a Glimm-type numerical scheme tailored to the exact Riemann solver and use it to reproduce the wave patterns obtained analytically.