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Numerical approximations 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), Italy 
2.  Istituto per le Applicazioni del Calcolo "M. Picone", IACCNR, Viale del Policlinico, 137, 00161, Roma, Italy 
3.  Istituto per le Applicazioni del Calcolo "M. Picone", IACCNR, Viale del Policlinico 137, 00161 Roma 
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Darko Mitrovic. New entropy conditions for scalar conservation laws with discontinuous flux. Discrete & Continuous Dynamical Systems  A, 2011, 30 (4) : 11911210. doi: 10.3934/dcds.2011.30.1191 
[2] 
Takeshi Fukao, Shuji Yoshikawa, Saori Wada. Structurepreserving finite difference schemes for the CahnHilliard equation with dynamic boundary conditions in the onedimensional case. Communications on Pure & Applied Analysis, 2017, 16 (5) : 19151938. doi: 10.3934/cpaa.2017093 
[3] 
Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 7388. doi: 10.3934/dcdss.2016.9.73 
[4] 
TaiPing Liu, ShihHsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete & Continuous Dynamical Systems  A, 2000, 6 (1) : 143145. doi: 10.3934/dcds.2000.6.143 
[5] 
Laurent Lévi, Julien Jimenez. Coupling of scalar conservation laws in stratified porous media. Conference Publications, 2007, 2007 (Special) : 644654. doi: 10.3934/proc.2007.2007.644 
[6] 
Georges Bastin, B. Haut, JeanMichel Coron, Brigitte d'AndréaNovel. Lyapunov stability analysis of networks of scalar conservation laws. Networks & Heterogeneous Media, 2007, 2 (4) : 751759. doi: 10.3934/nhm.2007.2.751 
[7] 
Raimund Bürger, Kenneth H. Karlsen, John D. Towers. On some difference schemes and entropy conditions for a class of multispecies kinematic flow models with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (3) : 461485. doi: 10.3934/nhm.2010.5.461 
[8] 
Bernard Ducomet, Alexander Zlotnik, Ilya Zlotnik. On a family of finitedifference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation. Kinetic & Related Models, 2009, 2 (1) : 151179. doi: 10.3934/krm.2009.2.151 
[9] 
Adimurthi , Shyam Sundar Ghoshal, G. D. Veerappa Gowda. Exact controllability of scalar conservation laws with strict convex flux. Mathematical Control & Related Fields, 2014, 4 (4) : 401449. doi: 10.3934/mcrf.2014.4.401 
[10] 
Maria Laura Delle Monache, Paola Goatin. Stability estimates for scalar conservation laws with moving flux constraints. Networks & Heterogeneous Media, 2017, 12 (2) : 245258. doi: 10.3934/nhm.2017010 
[11] 
Boris P. Andreianov, Giuseppe Maria Coclite, Carlotta Donadello. Wellposedness for vanishing viscosity solutions of scalar conservation laws on a network. Discrete & Continuous Dynamical Systems  A, 2017, 37 (11) : 59135942. doi: 10.3934/dcds.2017257 
[12] 
Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra. Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Networks & Heterogeneous Media, 2013, 8 (4) : 969984. doi: 10.3934/nhm.2013.8.969 
[13] 
Evgeny Yu. Panov. On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws. Networks & Heterogeneous Media, 2016, 11 (2) : 349367. doi: 10.3934/nhm.2016.11.349 
[14] 
Shijin Deng, Weike Wang. Pointwise estimates of solutions for the multidimensional scalar conservation laws with relaxation. Discrete & Continuous Dynamical Systems  A, 2011, 30 (4) : 11071138. doi: 10.3934/dcds.2011.30.1107 
[15] 
Darko Mitrovic, Ivan Ivec. A generalization of $H$measures and application on purely fractional scalar conservation laws. Communications on Pure & Applied Analysis, 2011, 10 (6) : 16171627. doi: 10.3934/cpaa.2011.10.1617 
[16] 
Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks & Heterogeneous Media, 2015, 10 (2) : 255293. doi: 10.3934/nhm.2015.10.255 
[17] 
Alexander Bobylev, Mirela Vinerean, Åsa Windfäll. Discrete velocity models of the Boltzmann equation and conservation laws. Kinetic & Related Models, 2010, 3 (1) : 3558. doi: 10.3934/krm.2010.3.35 
[18] 
Wen Shen. Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads. Networks & Heterogeneous Media, 2019, 14 (4) : 709732. doi: 10.3934/nhm.2019028 
[19] 
Christophe Prieur. Control of systems of conservation laws with boundary errors. Networks & Heterogeneous Media, 2009, 4 (2) : 393407. doi: 10.3934/nhm.2009.4.393 
[20] 
Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks & Heterogeneous Media, 2007, 2 (4) : 717731. doi: 10.3934/nhm.2007.2.717 
2018 Impact Factor: 0.871
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