The initial boundary value problem for second order traffic flow models with vacuum: Existence of entropy weak solutions

We study the IBVP for a non-strictly hyperbolic 2 × 2 system of conservation laws on an interval with characteristic boundaries, modelling traffic dynamics including vacuum states on a road stretch. After giving a detailed characterization of the admissible states at the boundary in terms of Riemann solver and entropy conditions, we prove existence of entropy weak solutions for data of bounded variation in the Riemann invariant coordinates by convergence of wave-front tracking approximations.