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. (C) 2018 Elsevier Inc. All rights reserved.