
-
Previous Article
Transport of measures on networks
- NHM Home
- This Issue
-
Next Article
Analysis and control on networks: Trends and perspectives
The Riemann solver for traffic flow at an intersection with buffer of vanishing size
1. | Department of Mathematics, Penn State University, University Park, Pa. 16802, USA |
2. | Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway |
The paper examines the model of traffic flow at an intersection introduced in [
References:
[1] |
A. Bressan, S. Canic, M. Garavello, M. Herty and B. Piccoli,
Flow on networks: Recent results and perspectives, EMS Surv. Math. Sci., 1 (2014), 47-111.
doi: 10.4171/EMSS/2. |
[2] |
A. Bressan and K. Nguyen,
Conservation law models for traffic flow on a network of roads, Netw. Heter. Media, 10 (2015), 255-293.
doi: 10.3934/nhm.2015.10.255. |
[3] |
A. Bressan and F. Yu,
Continuous Riemann solvers for traffic flow at a junction, Discr. Cont. Dyn. Syst., 35 (2015), 4149-4171.
doi: 10.3934/dcds.2015.35.4149. |
[4] |
G. M. Coclite, M. Garavello and B. Piccoli,
Traffic flow on a road network, SIAM J. Math. Anal., 36 (2005), 1862-1886.
doi: 10.1137/S0036141004402683. |
[5] |
M. Garavello, Conservation laws at a node, in Nonlinear Conservation Laws and Applications (eds A. Bressan, G. Q. Chen, M. Lewicka), The IMA Volumes in Mathematics and its Applications 153 (2011), 293-302.
doi: 10.1007/978-1-4419-9554-4_15. |
[6] |
M. Garavello and B. Piccoli,
Traffic Flow on Networks. Conservation Laws Models, AIMS Series on Applied Mathematics, Springfield, Mo., 2006. |
[7] |
M. Garavello and B. Piccoli,
Conservation laws on complex networks, Ann. Inst. H. Poincaré, 26 (2009), 1925-1951.
doi: 10.1016/j.anihpc.2009.04.001. |
[8] |
M. Herty, J. P. Lebacque and S. Moutari,
A novel model for intersections of vehicular traffic
flow, Netw. Heterog. Media, 4 (2009), 813-826.
doi: 10.3934/nhm.2009.4.813. |
[9] |
H. Holden and N. H. Risebro,
A mathematical model of traffic flow on a network of unidirectional roads, SIAM J. Math. Anal., 26 (1995), 999-1017.
doi: 10.1137/S0036141093243289. |
[10] |
C. Imbert, R. Monneau and H. Zidani,
A Hamilton-Jacobi approach to junction problems
and application to traffic flows, ESAIM-COCV, 19 (2013), 129-166.
doi: 10.1051/cocv/2012002. |
[11] |
P. Le Floch,
Explicit formula for scalar non-linear conservation laws with boundary condition, Math. Methods Appl. Sciences, 10 (1988), 265-287.
doi: 10.1002/mma.1670100305. |
[12] |
M. Lighthill and G. Whitham,
On kinematic waves. Ⅱ. A theory of traffic flow on long crowded
roads, Proceedings of the Royal Society of London: Series A, 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[13] |
P. I. Richards,
Shock waves on the highway, Oper. Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
show all references
References:
[1] |
A. Bressan, S. Canic, M. Garavello, M. Herty and B. Piccoli,
Flow on networks: Recent results and perspectives, EMS Surv. Math. Sci., 1 (2014), 47-111.
doi: 10.4171/EMSS/2. |
[2] |
A. Bressan and K. Nguyen,
Conservation law models for traffic flow on a network of roads, Netw. Heter. Media, 10 (2015), 255-293.
doi: 10.3934/nhm.2015.10.255. |
[3] |
A. Bressan and F. Yu,
Continuous Riemann solvers for traffic flow at a junction, Discr. Cont. Dyn. Syst., 35 (2015), 4149-4171.
doi: 10.3934/dcds.2015.35.4149. |
[4] |
G. M. Coclite, M. Garavello and B. Piccoli,
Traffic flow on a road network, SIAM J. Math. Anal., 36 (2005), 1862-1886.
doi: 10.1137/S0036141004402683. |
[5] |
M. Garavello, Conservation laws at a node, in Nonlinear Conservation Laws and Applications (eds A. Bressan, G. Q. Chen, M. Lewicka), The IMA Volumes in Mathematics and its Applications 153 (2011), 293-302.
doi: 10.1007/978-1-4419-9554-4_15. |
[6] |
M. Garavello and B. Piccoli,
Traffic Flow on Networks. Conservation Laws Models, AIMS Series on Applied Mathematics, Springfield, Mo., 2006. |
[7] |
M. Garavello and B. Piccoli,
Conservation laws on complex networks, Ann. Inst. H. Poincaré, 26 (2009), 1925-1951.
doi: 10.1016/j.anihpc.2009.04.001. |
[8] |
M. Herty, J. P. Lebacque and S. Moutari,
A novel model for intersections of vehicular traffic
flow, Netw. Heterog. Media, 4 (2009), 813-826.
doi: 10.3934/nhm.2009.4.813. |
[9] |
H. Holden and N. H. Risebro,
A mathematical model of traffic flow on a network of unidirectional roads, SIAM J. Math. Anal., 26 (1995), 999-1017.
doi: 10.1137/S0036141093243289. |
[10] |
C. Imbert, R. Monneau and H. Zidani,
A Hamilton-Jacobi approach to junction problems
and application to traffic flows, ESAIM-COCV, 19 (2013), 129-166.
doi: 10.1051/cocv/2012002. |
[11] |
P. Le Floch,
Explicit formula for scalar non-linear conservation laws with boundary condition, Math. Methods Appl. Sciences, 10 (1988), 265-287.
doi: 10.1002/mma.1670100305. |
[12] |
M. Lighthill and G. Whitham,
On kinematic waves. Ⅱ. A theory of traffic flow on long crowded
roads, Proceedings of the Royal Society of London: Series A, 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[13] |
P. I. Richards,
Shock waves on the highway, Oper. Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |




[1] |
Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 185-195. doi: 10.3934/dcds.2009.23.185 |
[2] |
Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure and Applied Analysis, 2013, 12 (2) : 755-769. doi: 10.3934/cpaa.2013.12.755 |
[3] |
Yu Zhang, Yanyan Zhang. Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1523-1545. doi: 10.3934/cpaa.2019073 |
[4] |
João-Paulo Dias, Mário Figueira. On the Riemann problem for some discontinuous systems of conservation laws describing phase transitions. Communications on Pure and Applied Analysis, 2004, 3 (1) : 53-58. doi: 10.3934/cpaa.2004.3.53 |
[5] |
Zhi-Qiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initial-boundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure and Applied Analysis, 2015, 14 (3) : 759-792. doi: 10.3934/cpaa.2015.14.759 |
[6] |
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 |
[7] |
Weishi Liu. Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 871-884. doi: 10.3934/dcds.2004.10.871 |
[8] |
Mauro Garavello, Francesca Marcellini. The Riemann Problem at a Junction for a Phase Transition Traffic Model. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5191-5209. doi: 10.3934/dcds.2017225 |
[9] |
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 |
[10] |
Alberto Bressan, Fang Yu. Continuous Riemann solvers for traffic flow at a junction. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4149-4171. doi: 10.3934/dcds.2015.35.4149 |
[11] |
Boris Andreianov, Mohamed Karimou Gazibo. Explicit formulation for the Dirichlet problem for parabolic-hyperbolic conservation laws. Networks and Heterogeneous Media, 2016, 11 (2) : 203-222. doi: 10.3934/nhm.2016.11.203 |
[12] |
Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 |
[13] |
Tatsien Li, Wancheng Sheng. The general multi-dimensional Riemann problem for hyperbolic systems with real constant coefficients. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 737-744. doi: 10.3934/dcds.2002.8.737 |
[14] |
Rinaldo M. Colombo, Mauro Garavello. A Well Posed Riemann Problem for the $p$--System at a Junction. Networks and Heterogeneous Media, 2006, 1 (3) : 495-511. doi: 10.3934/nhm.2006.1.495 |
[15] |
Vladimir S. Gerdjikov, Rossen I. Ivanov, Aleksander A. Stefanov. Riemann-Hilbert problem, integrability and reductions. Journal of Geometric Mechanics, 2019, 11 (2) : 167-185. doi: 10.3934/jgm.2019009 |
[16] |
Meixiang Huang, Zhi-Qiang Shao. Riemann problem for the relativistic generalized Chaplygin Euler equations. Communications on Pure and Applied Analysis, 2016, 15 (1) : 127-138. doi: 10.3934/cpaa.2016.15.127 |
[17] |
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673 |
[18] |
Gui-Qiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1011-1036. doi: 10.3934/cpaa.2011.10.1011 |
[19] |
Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2003, 2 (1) : 51-64. doi: 10.3934/cpaa.2003.2.51 |
[20] |
Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 717-731. doi: 10.3934/nhm.2007.2.717 |
2021 Impact Factor: 1.41
Tools
Metrics
Other articles
by authors
[Back to Top]