On the approximation of the solutions of the Riemann problem for a discontinuous conservation law

For a class of discontinuous flux functions introduced in [3] (cf. also [4]), we prove, for the Riemann problem, an extension of the existence result proved in [2] for a Lipschitz continuous flux function. In the last section, and based in the previous results, we apply the Lax-Friedrichs approximation method and the limiters technique (cf.[6]) to compute the quoted solution in a numerical example. For related results see [5].