Institutional Repository
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/90C153F1-DF79-40F6-BE29-1EFDE2F353B6 | ||
| Year | 2024 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | D. Theodosis, I. Karafyllis, G. Titakis, I. Papamichail and M. Papageorgiou, “A nonlinear heat equation arising from automated-vehicle traffic flow models,” J. Comput. Appl. Math., 2023, doi: 10.1016/j.cam.2023.115443. https://doi.org/10.1016/j.cam.2023.115443 | ||
| Appears in Collections |
In this paper, a new nonlinear heat equation is studied that arises as a model of the collective behaviour 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–Whitham–Richards (LWR) model are provided, illustrating the benefits of the use of automated vehicles.
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