Math. Model. Nat. Phenom.
Volume 18, 2023
|Number of page(s)||25|
|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. [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. [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. [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. [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. [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. [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. [Google Scholar]
- H. Lenz, C. Wagner and R. Sollacher Multi-anticipative car-following model. Eur. Phys. J. B 7 (1999) 331–335. [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. [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. [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. [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. [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. [Google Scholar]
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