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Car-following and the macroscopic Aw-Rascle traffic flow model
1. | Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway, Norway |
[1] |
Eugen Stumpf. On a delay differential equation arising from a car-following model: Wavefront solutions with constant-speed and their stability. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3317-3340. doi: 10.3934/dcdsb.2017139 |
[2] |
Tong Li, Nitesh Mathur. Riemann problem for a non-strictly hyperbolic system in chemotaxis. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2173-2187. doi: 10.3934/dcdsb.2021128 |
[3] |
Wenming Hu, Huicheng Yin. Well-posedness of low regularity solutions to the second order strictly hyperbolic equations with non-Lipschitzian coefficients. Communications on Pure and Applied Analysis, 2019, 18 (4) : 1891-1919. doi: 10.3934/cpaa.2019088 |
[4] |
Anupam Sen, T. Raja Sekhar. Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 931-942. doi: 10.3934/cpaa.2019045 |
[5] |
Florent Berthelin, Paola Goatin. Regularity results for the solutions of a non-local model of traffic flow. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3197-3213. doi: 10.3934/dcds.2019132 |
[6] |
Felisia Angela Chiarello, Paola Goatin. Non-local multi-class traffic flow models. Networks and Heterogeneous Media, 2019, 14 (2) : 371-387. doi: 10.3934/nhm.2019015 |
[7] |
Tai-Ping Liu, Zhouping Xin, Tong Yang. Vacuum states for compressible flow. Discrete and Continuous Dynamical Systems, 1998, 4 (1) : 1-32. doi: 10.3934/dcds.1998.4.1 |
[8] |
Yongluo Cao, Stefano Luzzatto, Isabel Rios. Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 61-71. doi: 10.3934/dcds.2006.15.61 |
[9] |
Tong Li, Kun Zhao. On a quasilinear hyperbolic system in blood flow modeling. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 333-344. doi: 10.3934/dcdsb.2011.16.333 |
[10] |
Jingmei Zhou, Xiangmo Zhao, Xin Cheng, Zhigang Xu. Visualization analysis of traffic congestion based on floating car data. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1423-1433. doi: 10.3934/dcdss.2015.8.1423 |
[11] |
Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4619-4635. doi: 10.3934/dcds.2016001 |
[12] |
Jan Friedrich, Oliver Kolb, Simone Göttlich. A Godunov type scheme for a class of LWR traffic flow models with non-local flux. Networks and Heterogeneous Media, 2018, 13 (4) : 531-547. doi: 10.3934/nhm.2018024 |
[13] |
Alexander Kurganov, Anthony Polizzi. Non-oscillatory central schemes for traffic flow models with Arrhenius look-ahead dynamics. Networks and Heterogeneous Media, 2009, 4 (3) : 431-451. doi: 10.3934/nhm.2009.4.431 |
[14] |
Paola Goatin, Sheila Scialanga. Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity. Networks and Heterogeneous Media, 2016, 11 (1) : 107-121. doi: 10.3934/nhm.2016.11.107 |
[15] |
Stefano Bianchini. On the shift differentiability of the flow generated by a hyperbolic system of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 329-350. doi: 10.3934/dcds.2000.6.329 |
[16] |
Yacine Chitour, Benedetto Piccoli. Traffic circles and timing of traffic lights for cars flow. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 599-630. doi: 10.3934/dcdsb.2005.5.599 |
[17] |
Maria Laura Delle Monache, Paola Goatin. A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 435-447. doi: 10.3934/dcdss.2014.7.435 |
[18] |
Tong Tang, Yongfu Wang. Strong solutions to compressible barotropic viscoelastic flow with vacuum. Kinetic and Related Models, 2015, 8 (4) : 765-775. doi: 10.3934/krm.2015.8.765 |
[19] |
Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Corrigendum to "Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology". Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4585-4586. doi: 10.3934/dcds.2017196 |
[20] |
Tomasz Downarowicz, Benjamin Weiss. Pure strictly uniform models of non-ergodic measure automorphisms. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 863-884. doi: 10.3934/dcds.2021140 |
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