Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 18, 2023
|
|
---|---|---|
Article Number | 7 | |
Number of page(s) | 25 | |
Section | Mathematical methods | |
DOI | https://doi.org/10.1051/mmnp/2023006 | |
Published online | 10 March 2023 |
- M. Al Haj, N. Forcadel and R. Monneau Existence and uniqueness of traveling waves for fully overdamped Frenkel—Kontorova models. Arch. Ratl. Mech. Anal. 210 (2013) 45–99. [CrossRef] [Google Scholar]
- M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51 (1995) 1035. [CrossRef] [Google Scholar]
- G. Barles, An introduction to the theory of viscosity solutions for first-order hamilton—jacobi equations and applications, in Hamilton-Jacobi equations: approximations, numerical analysis and applications. Springer (2013), pp. 49–109. [CrossRef] [Google Scholar]
- M. Brackstone and M. McDonald Car-following: a historical review. Transp. Res. F 2 (1999) 181–196. [CrossRef] [Google Scholar]
- M.G. Crandall, H. Ishii and P.-L. Lions User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27 (1992) 1–67. [Google Scholar]
- M.G. Crandall and P.-L. Lions Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277 (1983) 1–42. [CrossRef] [Google Scholar]
- N. El Khatib, N. Forcadel and M. Zaydan Homogenization of a microscopic pedestrians model on a convergent junction. Math. Model. Nat. Phenom. 17 (2022) 21. [CrossRef] [EDP Sciences] [Google Scholar]
- N. El Khatib, N. Forcadel and M. Zaydan, Semidiscrete shocks for the full velocity difference model (2022). [Google Scholar]
- N. Forcadel, C. Imbert and R. Monneau Homogenization of fully overdamped Frenkel—Kontorova models. J. Differ. Equ. 246 (2009) 1057–1097. [CrossRef] [Google Scholar]
- A. Ghorbel and R. Monneau Existence and nonexistence of semidiscrete shocks for a car-following model in traffic flow. SIAM J. Math. Anal. 46 (2014) 3612–3639. [CrossRef] [MathSciNet] [Google Scholar]
- G.-S. Jiang and S.-H. Yu Discrete shocks for finite difference approximations to scalar conservation laws. SIAM J. Numer. Anal. 35 (1998) 749–772. [CrossRef] [MathSciNet] [Google Scholar]
- H. Lenz, C. Wagner and R. Sollacher Multi-anticipative car-following model. Eur. Phys. J. B 7 (1999) 331–335. [CrossRef] [Google Scholar]
- M.J. Lighthill and G.B. Whitham On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. Royal Soc. London Ser. A 229 (1955) 317–345. [MathSciNet] [Google Scholar]
- T.-P. Liu and S.-H. Yu Continuum shock profiles for discrete conservation laws I: Construction. Commun. Pure Appl. Math. A 52 (1999) 85–127. [CrossRef] [Google Scholar]
- A. Majda and J. Ralston Discrete shock profiles for systems of conservation laws. Commun. Pure Appl. Math. 32 (1979) 445–482. [CrossRef] [Google Scholar]
- G.F. Newell Nonlinear effects in the dynamics of car following. Oper. Res. 9 (1961) 209–229. [CrossRef] [Google Scholar]
- L.A. Pipes An operational analysis of traffic dynamics. J. Appl. Phys. 24 (1953) 274–281. [CrossRef] [MathSciNet] [Google Scholar]
- P.I. Richards Shock waves on the highway. Oper. Res. 4 (1956) 42–51. [CrossRef] [Google Scholar]
- J. Ridder and W. Shen Traveling waves for nonlocal models of traffic flow. Discr. Continu. Dyn. Syst. 39 (2019) 4001. [CrossRef] [Google Scholar]
- W. Shen Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition. Netw. Heterogeneous Media 13 (2018) 449. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S.-I. Tadaki and S. Yukawa Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam. New J. Phys. 10 (2008) 033001. [CrossRef] [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.