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Conservation Laws with Nonlocality in Density and Velocity and Their Applicability in Traffic Flow Modelling

Friedrich J, Göttlich S, Keimer A, Pflug L (2024)

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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.

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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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