Existence of BV solutions for a non-conservative constrained Aw–Rascle–Zhang model for vehicular traffic

The main aim of this paper is to study the Aw–Rascle–Zhang (ARZ) model with non-conservative local point constraint on the density flux introduced in [10], its motivation being, for instance, the modeling of traffic across a toll gate. We prove the existence of weak solutions under assumptions that result to be more general than those required in [11]. More precisely, we do not require that the waves of the first characteristic family have strictly negative speeds of propagation. The result is achieved by showing the convergence of a sequence of approximate solutions constructed via the wave-front tracking algorithm. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions.