We present a model for a class of non-local conservation laws arising in traffic flow modelling at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes (hence their maximal vehicle density). We use an upwind type numerical scheme to construct a sequence of approximate solutions, and we provide uniform L∞ and total variation estimates. In particular, the solutions of the proposed model stay positive and below the maximum density of each road segment. Using a Lax–Wendroff type argument and the doubling of variables technique, we prove the well-posedness of the proposed model. Finally, some numerical simulations are provided and compared with the corresponding (discontinuous) local model.

中文翻译：

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1对1路口的非本地交通流模型

我们提出了一个模型，用于在道路交叉口的交通流建模中出现的一类非局部守恒律。我们不考虑整条道路的单一速度函数，而是考虑两个不同的路段，它们的速度规律和车道数量可能不同（因此它们的最大车辆密度）。我们使用迎风型数值方案来构造一系列近似解，并提供统一的大号∞和总变异估计。特别是，所提出的模型的解决方案保持正数并且低于每个路段的最大密度。使用 Lax-Wendroff 类型参数和变量加倍技术，我们证明了所提出模型的适定性。最后，提供了一些数值模拟，并与相应的（不连续的）局部模型进行了比较。