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

10/09/2022

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by Dionysis Theodosis, et al.

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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.

Dionysis Theodosis
1 publication
Iasson Karafyllis
3 publications
George Titakis
1 publication
Ioannis Papamichail
1 publication
Markos Papageorgiou
2 publications

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