The continuum limit of non-local follow-the-leader models

DOI10.1051/M2AN/2024054MaRDI QIDQ6619604

Helge Holden, N. H. Risebro

Publication date: 16 October 2024

Published in: European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

continuum limitLighthill-Whitham-Richards modeltraffic flowfollow-the-leader model

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) First-order hyperbolic equations (35L02) Traffic and pedestrian flow models (76A30)

Cites Work

• On the micro-to-macro limit for first-order traffic flow models on networks
• Macroscopic models for vehicular flows and crowd dynamics: theory and applications. Classical and non-classical advanced mathematics for real life applications
• On the micro-macro limit in traffic flow
• A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit
• The continuum limit of follow-the-leader models -- a short proof
• Deterministic particle approximation of scalar conservation laws
• Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit
• Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow
• A justification of a LWR model based on a follow the leader description
• A Rigorous Treatment of a Follow-the-Leader Traffic Model with Traffic Lights Present
• Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
• Recent results on the singular local limit for nonlocal conservation laws
• On the Microscopic Modeling of Vehicular Traffic on General Networks
• Shock Waves on the Highway
• On kinematic waves II. A theory of traffic flow on long crowded roads
• Front tracking for hyperbolic conservation laws
• A general result on the approximation of local conservation laws by nonlocal conservation laws: the singular limit problem for exponential kernels
• The one-sided lipschitz condition in the follow-the-leader approximation of scalar conservation laws

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