Nonlocal balance laws–an overview over recent results

A Keimer, L Pflug - Handbook of Numerical Analysis, 2023 - Elsevier
In this contribution we give a short overview of recent advances in nonlocal conservation
laws. In these equations, we assume that the flux f is decomposable into f (x)= V (x) x, x∈ R …

An overview of non-local traffic flow models

FA Chiarello - Mathematical Descriptions of Traffic Flow: Micro, Macro …, 2021 - Springer
We give an overview of mathematical traffic flow models with non-local velocity. More
precisely, we consider conservation laws with flux functions depending on an integral …

On traffic flow with nonlocal flux: a relaxation representation

A Bressan, W Shen - Archive for Rational Mechanics and Analysis, 2020 - Springer
We consider a conservation law model of traffic flow, where the velocity of each car depends
on a weighted average of the traffic density ρ ρ ahead. The averaging kernel is of …

A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels

GM Coclite, JM Coron, N De Nitti, A Keimer… - Annales de l'Institut …, 2022 - ems.press
We deal with the problem of approximating a scalar conservation law by a conservation law
with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential …

Micro-macro limit of a nonlocal generalized Aw-Rascle type model

FA Chiarello, J Friedrich, P Goatin, S Göttlich - SIAM Journal on Applied …, 2020 - SIAM
We introduce a Follow-the-Leader approximation of a nonlocal generalized Aw--Rascle--
Zhang (GARZ) model for traffic flow. We prove the convergence to weak solutions of the …

Modeling multilane traffic with moving obstacles by nonlocal balance laws

A Bayen, J Friedrich, A Keimer, L Pflug… - SIAM Journal on Applied …, 2022 - SIAM
We consider a system of nonlocal balance laws where each balance law is coupled with the
remaining balance laws both by a nonlocal velocity function that takes into account the …

On the accuracy of the finite volume approximations to nonlocal conservation laws

A Aggarwal, H Holden, G Vaidya - Numerische Mathematik, 2024 - Springer
In this article, we discuss the error analysis for a certain class of monotone finite volume
schemes approximating nonlocal scalar conservation laws, modeling traffic flow and crowd …

Conservation laws with nonlocal velocity: the singular limit problem

J Friedrich, S Göttlich, A Keimer, L Pflug - SIAM Journal on Applied …, 2024 - SIAM
We consider conservation laws with nonlocal velocity and show, for nonlocal weights of
exponential type, that the unique solutions converge in a weak or strong sense (dependent …

A non-local traffic flow model for 1-to-1 junctions

FA Chiarello, J Friedrich, P Goatin… - European Journal of …, 2020 - cambridge.org
We present a model for a class of non-local conservation laws arising in traffic flow
modelling at road junctions. Instead of a single velocity function for the whole road, we …

Traveling waves for nonlocal models of traffic flow

J Ridder, W Shen - arXiv preprint arXiv:1808.03734, 2018 - arxiv.org
We consider several non-local models for traffic flow, including both microscopic ODE
models and macroscopic PDE models. The ODE models describe the movement of …