2026/07/16 by Debora Amadori, Felisia Angela Chiarello, Gianmarco Cipollone +2
#math.AP
In this paper, we study a system of nonlocal conservation laws motivated by traffic flow: a nonlocal version of the generalized Aw-Rascle-Zhang (GARZ) model. The nonlocality arises from downstream spatial averaging of the velocity by a one-sided kernel. We prove the existence and uniqueness of weak solutions for initial data of bounded variation via a fixed-point argument in the nonlocal velocity. We also establish stability with respect to the initial datum and an approximation of weak solutions by strong solutions in L1. Under additional, physically meaningful assumptions on the velocity and the initial datum, we obtain either a maximum principle for the density or invariant-region estimates. Finally, we study the singular limit as the nonlocal kernel converges to a Dirac distribution. Indeed, under additional assumptions, convergence to the unique local entropy solution can be proved. Some numerical simulations are provided, and the paper concludes with a discussion of open problems.