A nonlocal Aw-Rascle-Zhang system with linear pressure term

In this paper, we study a nonlocal extension of the Aw-Rascle-Zhang traffic model, where the pressure-like term is modeled as a convolution between vehicle density and a kernel function. This formulation captures nonlocal driver interactions and aligns structurally with the Euler-alignment system studied in (Leslie and Tan in Commun. Partial Differ. Equ. 48(5):753–791, 2023 ). Using a sticky particle approximation, we construct entropy weak solutions to the equation for the cumulative density and prove convergence of approximate solutions to weak solutions of the nonlocal system. The analysis includes well-posedness, stability estimates, and an entropic selection principle.