Abstract
In this work, we propose a non-local Hamilton–Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaled microscopic model. We also propose a numerical scheme and we prove an estimate error between the continuous solution of this problem and the numerical one. Finally, we provide some numerical illustrations.
Highlights
Traffic flow modelling is an important challenge and has known an important development in the last decades
The link between conservation laws and Hamilton–Jacobi equations has been known to mathematicians for decades [21, 25, 30], but was brought up to the attention of the traffic flow theory community just recently by [10, 11]
We proposed and study a non-local traffic flow model starting from the microscopic model to build the homogenized macroscopic model
Summary
Traffic flow modelling is an important challenge and has known an important development in the last decades. The most popular model is the LWR model (see [28, 31]) This model, expressed in the Eulerian coordinates, describes the dynamics of the density of vehicles. Since these pioneering works, a lot of models have been proposed and we refer to [17] for an overview of these models. We propose a new non-local macroscopic model This model is expressed in the lagrangian coordinates at the Hamilton–Jacobi level.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: ESAIM: Mathematical Modelling and Numerical Analysis
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
