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<p>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, <CitationRef CitationID="CR24">2023</CitationRef>). 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月6日

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  • Debora Amadori,
  • Felisia Angela Chiarello,
  • Gianmarco Cipollone

摘要

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.