Abstract

In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential equation (PDE) model for traffic flow. We demonstrate the well-posedness of the Lagrangian model in the \(L^1\) sense. Additionally, we rigorously show that our model coincides with the Lagrangian formulation of the local LWR model in the “zero-filter” (nonlocal-to-local) limit. We present numerical simulations of the new model. One significant advantage of the proposed model is that it allows for simple proofs of (i) estimates that do not depend on the “filter size” and (ii) the dissipation of an arbitrary convex entropy.

中文翻译：

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非局部拉格朗日交通流模型和零过滤极限

摘要

在本研究中，我们从交通流的“跟随领导者”模型开始，该模型基于下游汽车密度的加权调和平均值（在拉格朗日坐标中）。这产生了交通流的非局部拉格朗日偏微分方程 (PDE) 模型。我们证明了拉格朗日模型在\(L^1\)意义上的适定性。此外，我们严格证明我们的模型在“零滤波器”（非局部到局部）限制下与局部 LWR 模型的拉格朗日公式一致。我们提出了新模型的数值模拟。所提出模型的一个显着优点是它允许简单证明（i）不依赖于“滤波器大小”的估计和（ii）任意凸熵的耗散。