A nonlinear heat equation arising from automated-vehicle traffic flow modelsA nonlinear heat equation arising from automated-vehicle traffic flow models Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2024-06-282024enIn 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.The research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 Research and Innovation programme/ ERC Grant Agreement n. [833915], project TrafficFluid.http://creativecommons.org/licenses/by-nc-nd/4.0/Journal of Computational and Applied Mathematics437Theodosis_et_al_J. Comput. Appl. Math._2024_manuscript.pdfChania [Greece]Library of TUC2024-06-25application/pdf1.6 MBfree Theodosis Dionysios Θεοδοσης-Παλιμερης Διονυσιος Karafyllis Iason Καραφυλλης Ιασων Titakis Georgios Τιτακης Γεωργιος Papamichail Ioannis Παπαμιχαηλ Ιωαννης Papageorgiou Markos Παπαγεωργιου Μαρκος Elsevier Nonlinear heat equation Macroscopic traffic flow Automated vehicles