Conservation Laws with Nonlocality in Density and Velocity and Their Applicability in Traffic Flow Modelling
Friedrich J, Göttlich S, Keimer A, Pflug L (2024)
Publication Language: English
Publication Type: Conference contribution, Conference Contribution
Publication year: 2024
Publisher: Springer
Series: SEMA SIMAI
City/Town: Cham
Book Volume: 35
Pages Range: 347-357
Conference Proceedings Title: Hyperbolic Problems: Theory, Numerics, Applications. Volume II
Event location: Málaga
ISBN: 978-3-031-55263-2
DOI: 10.1007/978-3-031-55264-9_30
Abstract
In this work we present a nonlocal conservation law with a velocity depending on an integral term over a part of the space. The model class covers already existing models in literature, but it is also able to describe new dynamics mainly arising in the context of traffic flow modelling. We prove the existence and uniqueness of weak solutions of the nonlocal conservation law. Further, we provide a suitable numerical discretization and present numerical examples.
Authors with CRIS profile
Alexander Keimer
Professur für Mathematik (Analysis)
Lukas Pflug
FAU Competence Center Scientific Computing (FAU CSC)
Involved external institutions
Universität Mannheim
Germany (DE)
Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen
Germany (DE)
Germany (DE)
Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen
Germany (DE)
How to cite
APA:
Friedrich, J., Göttlich, S., Keimer, A., & Pflug, L. (2024). Conservation Laws with Nonlocality in Density and Velocity and Their Applicability in Traffic Flow Modelling. In Carlos Parés, Manuel J. Castro, Tomás Morales de Luna, María Luz Muñoz-Ruiz (Eds.), Hyperbolic Problems: Theory, Numerics, Applications. Volume II (pp. 347-357). Málaga, ES: Cham: Springer.
MLA:
Friedrich, Jan, et al. "Conservation Laws with Nonlocality in Density and Velocity and Their Applicability in Traffic Flow Modelling." Proceedings of the HYP 2022 - XVIII International Conference on Hyperbolic Problems, Málaga Ed. Carlos Parés, Manuel J. Castro, Tomás Morales de Luna, María Luz Muñoz-Ruiz, Cham: Springer, 2024. 347-357.
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