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arXiv · 2210.04321

A Nonlinear Heat Equation Arising from Automated-Vehicle Traffic Flow Models

Dionysis Theodosis·Iasson Karafyllis·George Titakis·Ioannis Papamichail·Markos Papageorgiou
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Abstract

In this paper, a new nonlinear heat equation is studied that arises as a model of the collective behavior of automated vehicles. The properties of the solutions of this equation are studied by introducing the appropriate notion of a weak solution that requires certain entropy-like conditions. To obtain an approximation of the solution of the nonlinear heat equation, a new conservative first-order finite difference scheme is proposed that respects the corresponding entropy conditions, and certain links between the weak solution and the numerical scheme are provided. Finally, a traffic simulation scenario and a comparison with the Lighthill-Witham-Richards (LWR) model are provided, illustrating the benefits of the use of automated vehicles.

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Dionysis Theodosis, Iasson Karafyllis, George Titakis, Ioannis Papamichail, Markos Papageorgiou. 2022-10-09. A Nonlinear Heat Equation Arising from Automated-Vehicle Traffic Flow Models. https://arxiv.org/abs/2210.04321

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