Open Access
Issue |
ESAIM: M2AN
Volume 59, Number 4, July-August 2025
|
|
---|---|---|
Page(s) | 2021 - 2054 | |
DOI | https://doi.org/10.1051/m2an/2025051 | |
Published online | 17 July 2025 |
- S.S.G. Adimurthi, R. Dutta and G.D. Veerappa Gowda, Existence and nonexistence of TV bounds for scalar conservation laws with discontinuous flux. Commun. Pure Appl. Math. 64 (2011) 84–115. [Google Scholar]
- B. Andreianov, K.H. Karlsen and N.H. Risebro, A theory of L1-dissipative solvers for scalar conservation laws with discontinuous flux. Arch. Ration. Mech. Anal. 201 (2011) 27–86. [Google Scholar]
- A. Aw, A. Klar, T. Materne and M. Rascle, Derivation of continuum traffic flow models from microscopic follow-the-leader models. SIAM J. Appl. Math. 63 (2002) 259–278. [Google Scholar]
- A. Bayen, M.L. Delle Monache, M. Garavello, P. Goatin and B. Piccoli, Control Problems for Conservation Laws with Traffic Applications: Modeling, Analysis, and Numerical Methods. Springer Nature (2022). [Google Scholar]
- A. Bressan, S. Canic, M. Garavello, H. Herty and P. Piccoli, Flows on networks: Recent results and perspectives. EMS Surv. Math. Sci. 1 (2014) 47–111. [Google Scholar]
- P. Cardaliaguet and N. Forcadel, Microscopic derivation of a traffic flow model with a bifurcation. Arch. Ration. Mech. Anal. 248 (2024) 6. [Google Scholar]
- P. Cardaliaguet, N. Forcadel, T. Girard and R. Monneau, Conservation law and Hamilton–Jacobi equations on a junction: the convex case. Preprint arXiv:2311.07177 (2023). [Google Scholar]
- P. Cardaliaguet, N. Forcadel and R. Monneau, A class of germs arising from homogenization in traffic flow on junctions. J. Hyperbolic Differ. Equ. 21 (2024) 189–254. [Google Scholar]
- F.A. Chiarello, J. Friedrich, P. Goatin and S. Göttlich, Micro-macro limit of a nonlocal generalized Aw-Rascle type model. SIAM J. Appl. Math. 80 (2020) 1841–1861. [CrossRef] [MathSciNet] [Google Scholar]
- M. Di Francesco and M.D. Rosini, Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit. Arch. Ration. Mech. Anal. 217 (2015) 831–871. [CrossRef] [MathSciNet] [Google Scholar]
- M. Di Francesco and G. Stivaletta, The one-sided lipschitz condition in the follow-the-leader approximation of scalar conservation laws. J. Hyperbolic Differ. Equ. 19 (2022) 775–807. [Google Scholar]
- M. Di Francesco, S. Fagioli, M.D. Rosini and G. Russo, A deterministic particle approximation for non-linear conservation laws, in XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications. Springer International Publishing, Cham (2016) 487–499. [Google Scholar]
- U.S. Fjordholm, M. Musch and N.H. Risebro, Well-posedness and convergence of a finite volume method for conservation laws on networks. SIAM J. Numer. Anal. 60 (2022) 606–630. [Google Scholar]
- N. Forcadel and W. Salazar, Homogenization of a discrete model for a bifurcation and application to traffic flow. Journal de Mathématiques Pures et Appliquées 136 (2020) 356–414. [Google Scholar]
- N. Forcadel, C. Imbert and R. Monneau, Homogenization of some particle systems with two-body interactions and of the dislocation dynamics. Discrete Contin. Dyn. Syst.-Ser. A 23 (2009) 785–826. [Google Scholar]
- N. Forcadel, W. Salazar and M. Zaydan, Specified homogenization of a discrete traffic model leading to an effective junction condition. Commun. Pure Appl. Anal. 17 (2018) 2173–2206. [CrossRef] [MathSciNet] [Google Scholar]
- N. Forcadel, C. Imbert and R. Monneau, Germs for scalar conservation laws: the Hamilton–Jacobi equation point of view. Preprint arXiv:2407.04318 (2024). [Google Scholar]
- M. Garavello, K. Han and B. Piccoli, Models for Vehicular Traffic on Networks. Vol. 9. American Institute of Mathematical Sciences (AIMS), Springfield, MO (2016). [Google Scholar]
- P. Goatin and F. Rossi, A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit. Commun. Math. Sci. 15 (2017) 261–287. [CrossRef] [MathSciNet] [Google Scholar]
- H. Holden and N.H. Risebro, The continuum limit of follow-the-leader models – a short proof. Discrete Contin. Dyn. Syst. 38 (2018) 715–722. [Google Scholar]
- C. Imbert and R. Monneau, Flux-limited solutions for quasi-convex Hamilton–Jacobi equations on networks. Annales scientifiques de l’ENS 50 (2017) 357–448. [Google Scholar]
- S.M. Kruzhkov, First order quasi-linear equations in several independent variables. Math. USSR Sbornik 10 (1970) 217–243. [Google Scholar]
- F. Marcellini, The follow-the-leader model without a leader: an infinite-dimensional Cauchy problem. J. Math. Anal. App. 495 (2021) 124664. [Google Scholar]
- S. Mishra, Chapter 18 – numerical methods for conservation laws with discontinuous coefficients, in Handbook of Numerical Methods for Hyperbolic Problems. Vol. 18 of Handbook of Numerical Analysis, edited by R. Abgrall and C.-W. Shu. Elsevier (2017) 479–506. [Google Scholar]
- M. Musch, U.S. Fjordholm and N.H. Risebro, Well-posedness theory for nonlinear scalar conservation laws on networks. Netw. Heterog. Media 17 (2022) 101–128. [Google Scholar]
- E.Y. Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws. J. Hyperbolic Differ. Equ. 4 (2007) 729–770. [Google Scholar]
- H.O. Storbugt, Convergence of rough follow-the-leader approximations and existence of weak solutions for the one-dimensional Hughes model. Discrete Contin. Dyn. Syst. 44 (2024) 2029–2067. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.