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Fast algorithms for the approximation of a traffic flow model on networks
1. | Department of Engineering of Information and Applied Mathematics, DIIMA, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA) |
2. | Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico, 137, 00161, Roma |
3. | Istituto per le Applicazioni del Calcolo, Viale del Policlinico 137, 00161 Rome, Italy |
[1] |
Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks and Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255 |
[2] |
Nicola Zamponi. Some fluid-dynamic models for quantum electron transport in graphene via entropy minimization. Kinetic and Related Models, 2012, 5 (1) : 203-221. doi: 10.3934/krm.2012.5.203 |
[3] |
Wen Shen. Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads. Networks and Heterogeneous Media, 2019, 14 (4) : 709-732. doi: 10.3934/nhm.2019028 |
[4] |
Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 73-88. doi: 10.3934/dcdss.2016.9.73 |
[5] |
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 |
[6] |
Raimund Bürger, Antonio García, Kenneth H. Karlsen, John D. Towers. Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model. Networks and Heterogeneous Media, 2008, 3 (1) : 1-41. doi: 10.3934/nhm.2008.3.1 |
[7] |
Laurent Lévi, Julien Jimenez. Coupling of scalar conservation laws in stratified porous media. Conference Publications, 2007, 2007 (Special) : 644-654. doi: 10.3934/proc.2007.2007.644 |
[8] |
Georges Bastin, B. Haut, Jean-Michel Coron, Brigitte d'Andréa-Novel. Lyapunov stability analysis of networks of scalar conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 751-759. doi: 10.3934/nhm.2007.2.751 |
[9] |
Claire david@lmm.jussieu.fr David, Pierre Sagaut. Theoretical optimization of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 286-293. doi: 10.3934/proc.2007.2007.286 |
[10] |
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 |
[11] |
Raimund Bürger, Kenneth H. Karlsen, John D. Towers. On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux. Networks and Heterogeneous Media, 2010, 5 (3) : 461-485. doi: 10.3934/nhm.2010.5.461 |
[12] |
Lih-Ing W. Roeger. Dynamically consistent discrete Lotka-Volterra competition models derived from nonstandard finite-difference schemes. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 415-429. doi: 10.3934/dcdsb.2008.9.415 |
[13] |
Adimurthi , Shyam Sundar Ghoshal, G. D. Veerappa Gowda. Exact controllability of scalar conservation laws with strict convex flux. Mathematical Control and Related Fields, 2014, 4 (4) : 401-449. doi: 10.3934/mcrf.2014.4.401 |
[14] |
Maria Laura Delle Monache, Paola Goatin. Stability estimates for scalar conservation laws with moving flux constraints. Networks and Heterogeneous Media, 2017, 12 (2) : 245-258. doi: 10.3934/nhm.2017010 |
[15] |
Boris P. Andreianov, Giuseppe Maria Coclite, Carlotta Donadello. Well-posedness for vanishing viscosity solutions of scalar conservation laws on a network. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5913-5942. doi: 10.3934/dcds.2017257 |
[16] |
Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra. Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Networks and Heterogeneous Media, 2013, 8 (4) : 969-984. doi: 10.3934/nhm.2013.8.969 |
[17] |
Evgeny Yu. Panov. On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws. Networks and Heterogeneous Media, 2016, 11 (2) : 349-367. doi: 10.3934/nhm.2016.11.349 |
[18] |
Shijin Deng, Weike Wang. Pointwise estimates of solutions for the multi-dimensional scalar conservation laws with relaxation. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 1107-1138. doi: 10.3934/dcds.2011.30.1107 |
[19] |
Darko Mitrovic. New entropy conditions for scalar conservation laws with discontinuous flux. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 1191-1210. doi: 10.3934/dcds.2011.30.1191 |
[20] |
Darko Mitrovic, Ivan Ivec. A generalization of $H$-measures and application on purely fractional scalar conservation laws. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1617-1627. doi: 10.3934/cpaa.2011.10.1617 |
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