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The continuum limit of Follow-the-Leader models --- a short proof

Discrete and Continuous Dynamical Systems  Volume 38, Issue 2, Pages : 715 - 722, 2017

Helge Holden - (email), Nils Henrik Risebro - (email)

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Symmetry analysis of a Lane-Emden-Klein-Gordon-Fock system with central symmetry

Discrete and Continuous Dynamical Systems - Series S  Volume 11, Issue 4, Pages : 667 - 673, 2017

Igor Freire - (email), Ben Muatjetjeja - (email)

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Capacity drop and traffic control for a second order traffic model

Networks and Heterogeneous Media  Volume 12, Issue 4, Pages : 663 - 681, 2017

Oliver Kolb - (email), Simone Göttlich - (email), Paola Goatin - (email)

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Analysis and control on networks: Trends and perspectives

Networks and Heterogeneous Media  Volume 12, Issue 3, Pages : i - ii, 2017

Fabio Ancona - (email), Laura Caravenna - (email), Annalisa Cesaroni - (email), Giuseppe Maria Coclite - (email), Claudio Marchi - (email), Andrea Marson - (email)

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Moving bottlenecks for the Aw-Rascle-Zhang traffic flow model

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 10, Pages : 3921 - 3952, 2017

Stefano Villa - (email), Paola Goatin - (email), Christophe Chalons - (email)

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6

Well-posedness for vanishing viscosity solutions of scalar conservation laws on a network

Discrete and Continuous Dynamical Systems  Volume 37, Issue 11, Pages : 5913 - 5942, 2017

Boris P. Andreianov - (email), Giuseppe Maria Coclite - (email), Carlotta Donadello - (email)

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7

Analysis and control on networks: Trends and perspectives

Networks and Heterogeneous Media  Volume 12, Issue 2, Pages : i - ii, 2017

Fabio Ancona - (email), Laura Caravenna - (email), Annalisa Cesaroni - (email), Giuseppe Maria Coclite - (email), Claudio Marchi - (email), Andrea Marson - (email)

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8

A macroscopic traffic model with phase transitions and local point constraints on the flow

Networks and Heterogeneous Media  Volume 12, Issue 2, Pages : 297 - 317, 2017

Mohamed Benyahia - (email), Massimiliano D. Rosini - (email)

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9

Semi-Markovian capacities in production network models

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 9, Pages : 3235 - 3258, 2017

Simone Göttlich - (email), Stephan Knapp - (email)

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10

A mathematical framework for delay analysis in single source networks

Networks and Heterogeneous Media  Volume 12, Issue 1, Pages : 113 - 145, 2017

Samitha Samaranayake - (email), Axel Parmentier - (email), Ethan Xuan - (email), Alexandre Bayen - (email)

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11

Homogenization of second order discrete model with local perturbation and application to traffic flow

Discrete and Continuous Dynamical Systems  Volume 37, Issue 3, Pages : 1437 - 1487, 2016

Nicolas Forcadel - (email), Wilfredo Salazar - (email), Mamdouh Zaydan - (email)

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Kinetic models for traffic flow resulting in a reduced space of microscopic velocities

Kinetic and Related Models  Volume 10, Issue 3, Pages : 823 - 854, 2016

Gabriella Puppo - (email), Matteo Semplice - (email), Andrea Tosin - (email), Giuseppe Visconti - (email)

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Deterministic particle approximation of the Hughes model in one space dimension

Kinetic and Related Models  Volume 10, Issue 1, Pages : 215 - 237, 2016

Marco Di Francesco - (email), Simone Fagioli - (email), Massimiliano Daniele Rosini - (email), Giovanni Russo - (email)

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14

On optimization of a highly re-entrant production system

Networks and Heterogeneous Media  Volume 11, Issue 3, Pages : 415 - 445, 2016

Ciro D'Apice - (email), Peter I. Kogut - (email), Rosanna Manzo - (email)

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15

The unsteady transonic small disturbance equation: Data on oblique curves

Discrete and Continuous Dynamical Systems  Volume 36, Issue 8, Pages : 4213 - 4225, 2016

Mary Chern - (email), Barbara Lee Keyfitz - (email)

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16

High-order finite-volume methods on locally-structured grids

Discrete and Continuous Dynamical Systems  Volume 36, Issue 8, Pages : 4247 - 4270, 2016

Phillip Colella - (email)

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New interaction estimates for the Baiti-Jenssen system

Networks and Heterogeneous Media  Volume 11, Issue 2, Pages : 263 - 280, 2016

Laura Caravenna - (email), Laura V. Spinolo - (email)

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BV regularity near the interface for nonuniform convex discontinuous flux

Networks and Heterogeneous Media  Volume 11, Issue 2, Pages : 331 - 348, 2016

Shyam Sundar Ghoshal - (email)

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On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws

Networks and Heterogeneous Media  Volume 11, Issue 2, Pages : 349 - 367, 2016

Evgeny Yu. Panov - (email)

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20

On the concentration of entropy for scalar conservation laws

Discrete and Continuous Dynamical Systems - Series S  Volume 9, Issue 1, Pages : 73 - 88, 2015

Stefano Bianchini - (email), Elio Marconi - (email)

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A nonlinear generalization of the Camassa-Holm equation with peakon solutions

DCDS Supplements  Volume 2015, Issue special, Pages : 29 - 37, 2015

Stephen C. Anco - (email), Elena Recio - (email), María L. Gandarias - (email), María S. Bruzón - (email)

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22

Linear model of traffic flow in an isolated network

DCDS Supplements  Volume 2015, Issue special, Pages : 670 - 677, 2015

Ángela Jiménez-Casas - (email), Aníbal Rodríguez-Bernal - (email)

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Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks

Networks and Heterogeneous Media  Volume 10, Issue 4, Pages : 749 - 785, 2015

Martin Gugat - (email), Alexander Keimer - (email), Günter Leugering - (email), Zhiqiang Wang - (email)

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24

Continuous Riemann solvers for traffic flow at a junction

Discrete and Continuous Dynamical Systems  Volume 35, Issue 9, Pages : 4149 - 4171, 2015

Alberto Bressan - (email), Fang Yu - (email)

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Structural analysis and traffic flow in the transport networks of Madrid

Networks and Heterogeneous Media  Volume 10, Issue 1, Pages : 127 - 148, 2015

Mary Luz Mouronte - (email), Rosa María Benito - (email)

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A hybrid model for traffic flow and crowd dynamics with random individual properties

Mathematical Biosciences and Engineering  Volume 12, Issue 2, Pages : 393 - 413, 2014

Veronika Schleper - (email)

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On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains

Networks and Heterogeneous Media  Volume 9, Issue 3, Pages : 501 - 518, 2014

Ciro D'Apice - (email), Peter I. Kogut - (email), Rosanna Manzo - (email)

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28

An easy-to-use algorithm for simulating traffic flow on networks: Theoretical study

Networks and Heterogeneous Media  Volume 9, Issue 3, Pages : 519 - 552, 2014

Maya Briani - (email), Emiliano Cristiani - (email)

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29

Optimization for a special class of traffic flow models: Combinatorial and continuous approaches

Networks and Heterogeneous Media  Volume 9, Issue 2, Pages : 315 - 334, 2014

Simone Göttlich - (email), Oliver Kolb - (email), Sebastian Kühn - (email)

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30

Newton's law for a trajectory of concentration of solutions to nonlinear Schrodinger equation

Communications on Pure and Applied Analysis  Volume 13, Issue 5, Pages : 1685 - 1718, 2014

Anatoli Babin - (email), Alexander Figotin - (email)

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31

Non-existence and non-uniqueness for multidimensional sticky particle systems

Kinetic and Related Models  Volume 7, Issue 2, Pages : 205 - 218, 2014

Alberto Bressan - (email), Truyen Nguyen - (email)

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32

An easy-to-use algorithm for simulating traffic flow on networks: Numerical experiments

Discrete and Continuous Dynamical Systems - Series S  Volume 7, Issue 3, Pages : 379 - 394, 2014

Gabriella Bretti - (email), Maya Briani - (email), Emiliano Cristiani - (email)

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33

Fundamental diagrams for kinetic equations of traffic flow

Discrete and Continuous Dynamical Systems - Series S  Volume 7, Issue 3, Pages : 449 - 462, 2014

Luisa Fermo - (email), Andrea Tosin - (email)

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34

The LWR traffic model at a junction with multibuffers

Discrete and Continuous Dynamical Systems - Series S  Volume 7, Issue 3, Pages : 463 - 482, 2014

Mauro Garavello - (email)

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35

Traffic light control: A case study

Discrete and Continuous Dynamical Systems - Series S  Volume 7, Issue 3, Pages : 483 - 501, 2014

Simone Göttlich - (email), Ute Ziegler - (email)

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36

Computing travel times from filtered traffic states

Discrete and Continuous Dynamical Systems - Series S  Volume 7, Issue 3, Pages : 557 - 578, 2014

Pierre-Emmanuel Mazaré - (email), Olli-Pekka Tossavainen - (email), Daniel B. Work - (email)

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37

A justification of a LWR model based on a follow the leader description

Discrete and Continuous Dynamical Systems - Series S  Volume 7, Issue 3, Pages : 579 - 591, 2014

Elena Rossi - (email)

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38

Stochastic heat equations with cubic nonlinearity and additive space-time noise in 2D

DCDS Supplements  Volume 2013, Issue special, Pages : 673 - 684, 2013

Henri Schurz - (email)

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39

Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes

Networks and Heterogeneous Media  Volume 8, Issue 4, Pages : 969 - 984, 2013

Giuseppe Maria Coclite - (email), Lorenzo di Ruvo - (email), Jan Ernest - (email), Siddhartha Mishra - (email)

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40

Coupling of microscopic and phase transition models at boundary

Networks and Heterogeneous Media  Volume 8, Issue 3, Pages : 649 - 661, 2013

Mauro Garavello - (email), Benedetto Piccoli - (email)

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41

Numerical discretization of Hamilton--Jacobi equations on networks

Networks and Heterogeneous Media  Volume 8, Issue 3, Pages : 685 - 705, 2013

Simone Göttlich - (email), Ute Ziegler - (email), Michael Herty - (email)

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42

Qualitative analysis of some PDE models of traffic flow

Networks and Heterogeneous Media  Volume 8, Issue 3, Pages : 773 - 781, 2013

Tong Li - (email)

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43

Markov Chain Monte Carlo based inverse modeling of traffic flows using GPS data

Networks and Heterogeneous Media  Volume 8, Issue 3, Pages : 803 - 824, 2013

Olli-Pekka Tossavainen - (email), Daniel B. Work - (email)

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44

Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws

Mathematical Control and Related Fields  Volume 3, Issue 2, Pages : 121 - 142, 2013

Mapundi K. Banda - (email), Michael Herty - (email)

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45

Vanishing viscosity approach to a system of conservation laws admitting $\delta''$ waves

Communications on Pure and Applied Analysis  Volume 12, Issue 5, Pages : 2091 - 2118, 2013

K. T. Joseph - (email), Manas R. Sahoo - (email)

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46

Mathematics of traveling waves in chemotaxis --Review paper--

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 3, Pages : 601 - 641, 2012

Zhi-An Wang - (email)

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47

Coupling of non-local driving behaviour with fundamental diagrams

Kinetic and Related Models  Volume 5, Issue 4, Pages : 843 - 855, 2012

Michael Herty - (email), Reinhard Illner - (email)

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48

Geometric singular perturbation approach to the existence and instability of stationary waves for viscous traffic flow models

Communications on Pure and Applied Analysis  Volume 12, Issue 3, Pages : 1501 - 1526, 2012

John M. Hong - (email), Cheng-Hsiung Hsu - (email), Bo-Chih Huang - (email), Tzi-Sheng Yang - (email)

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49

Convergence rates of zero diffusion limit on large amplitude solution to a conservation laws arising in chemotaxis

Kinetic and Related Models  Volume 5, Issue 3, Pages : 563 - 581, 2012

Hongyun Peng - (email), Lizhi Ruan - (email), Changjiang Zhu - (email)

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50

Front tracking approximations for slow erosion

Discrete and Continuous Dynamical Systems  Volume 32, Issue 5, Pages : 1481 - 1502, 2012

Debora Amadori - (email), Wen Shen - (email)

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51

Integrating factors and conservation laws for some Camassa-Holm type equations

Communications on Pure and Applied Analysis  Volume 11, Issue 4, Pages : 1421 - 1430, 2012

Marianna Euler - (email), Norbert Euler - (email)

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52

Shock formation in a traffic flow model with Arrhenius look-ahead dynamics

Networks and Heterogeneous Media  Volume 6, Issue 4, Pages : 681 - 694, 2011

Dong Li - (email), Tong Li - (email)

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53

Time-continuous production networks with random breakdowns

Networks and Heterogeneous Media  Volume 6, Issue 4, Pages : 695 - 714, 2011

Simone Göttlich - (email), Stephan Martin - (email), Thorsten Sickenberger - (email)

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54

Stochastic wave equations with cubic nonlinearity and Q-regular additive noise in $\mathbb{R}^2$

DCDS Supplements  Volume 2011, Issue Special, Pages : 1299 - 1308, 2011

Henri Schurz - (email)

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55

On the structure of solutions of nonlinear hyperbolic systems of conservation laws

Communications on Pure and Applied Analysis  Volume 10, Issue 4, Pages : 1011 - 1036, 2011

Gui-Qiang Chen - (email), Monica Torres - (email)

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56

Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements

Discrete and Continuous Dynamical Systems - Series S  Volume 4, Issue 5, Pages : 1167 - 1179, 2010

Yuri B. Gaididei - (email), Rainer Berkemer - (email), Carlos Gorria - (email), Peter L. Christiansen - (email), Atsushi Kawamoto - (email), Takahiro Shiga - (email), Mads P. Sørensen - (email), Jens Starke - (email)

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57

On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux

Networks and Heterogeneous Media  Volume 5, Issue 3, Pages : 461 - 485, 2010

Raimund Bürger - (email), Kenneth H. Karlsen - (email), John D. Towers - (email)

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A review of conservation laws on networks

Networks and Heterogeneous Media  Volume 5, Issue 3, Pages : 565 - 581, 2010

Mauro Garavello - (email)

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On vanishing viscosity approximation of conservation laws with discontinuous flux

Networks and Heterogeneous Media  Volume 5, Issue 3, Pages : 617 - 633, 2010

Boris Andreianov - (email), Kenneth H. Karlsen - (email), Nils H. Risebro - (email)

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60

On the effects of discontinuous capillarities for immiscible two-phase flows in porous media made of several rock-types

Networks and Heterogeneous Media  Volume 5, Issue 3, Pages : 635 - 647, 2010

Clément Cancès - (email)

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61

The computation of nonclassical shock waves with a heterogeneous multiscale method

Networks and Heterogeneous Media  Volume 5, Issue 3, Pages : 661 - 674, 2010

Frederike Kissling - (email), Christian Rohde - (email)

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An overview on some results concerning the transport equation and its applications to conservation laws

Communications on Pure and Applied Analysis  Volume 9, Issue 5, Pages : 1283 - 1293, 2010

Gianluca Crippa - (email), Laura V. Spinolo - (email)

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63

Analytical and numerical investigations of refined macroscopic traffic flow models

Kinetic and Related Models  Volume 3, Issue 2, Pages : 311 - 333, 2010

Michael Herty - (email), Reinhard Illner - (email)

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64

Existence and stability of a multidimensional scalar conservation law with discontinuous flux

Networks and Heterogeneous Media  Volume 5, Issue 1, Pages : 163 - 188, 2010

Darko Mitrovic - (email)

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Discrete velocity models of the Boltzmann equation and conservation laws

Kinetic and Related Models  Volume 3, Issue 1, Pages : 35 - 58, 2010

Alexander Bobylev - (email), Mirela Vinerean - (email), Åsa Windfäll - (email)

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Solutions with large total variation to nonconservative hyperbolic systems

Communications on Pure and Applied Analysis  Volume 9, Issue 1, Pages : 47 - 60, 2009

Rinaldo M. Colombo - (email), Francesca Monti - (email)

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Decentralized optimal routing for packets flow on data networks

Discrete and Continuous Dynamical Systems - Series B  Volume 13, Issue 1, Pages : 59 - 78, 2009

A. Cascone - (email), Alessia Marigo - (email), B. Piccoli - (email), L. Rarità - (email)

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A novel model for intersections of vehicular traffic flow

Networks and Heterogeneous Media  Volume 4, Issue 4, Pages : 813 - 826, 2009

Michael Herty - (email), J.-P. Lebacque - (email), S. Moutari - (email)

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Non-oscillatory central schemes for traffic flow models with Arrhenius look-ahead dynamics

Networks and Heterogeneous Media  Volume 4, Issue 3, Pages : 431 - 451, 2009

Alexander Kurganov - (email), Anthony Polizzi - (email)

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Critical thresholds in a relaxation system with resonance of characteristic speeds

Discrete and Continuous Dynamical Systems  Volume 24, Issue 2, Pages : 511 - 521, 2009

Tong Li - (email), Hailiang Liu - (email)

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1D numerical simulation of the mep mathematical model in ballistic diode problem

Kinetic and Related Models  Volume 2, Issue 1, Pages : 81 - 107, 2009

Alexander Blokhin - (email), Alesya Ibragimova - (email)

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On Stop-and-Go waves in dense traffic

Kinetic and Related Models  Volume 1, Issue 3, Pages : 437 - 452, 2008

Michael Herty - (email), Reinhard Illner - (email)

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Stability of under-compressive waves with second and fourth order diffusions

Discrete and Continuous Dynamical Systems  Volume 22, Issue 3, Pages : 629 - 662, 2008

Changbing Hu - (email)

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Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model

Networks and Heterogeneous Media  Volume 3, Issue 1, Pages : 1 - 41, 2008

Raimund Bürger - (email), Antonio García - (email), Kenneth H. Karlsen - (email), John D. Towers - (email)

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A continuum-discrete model for supply chains dynamics

Networks and Heterogeneous Media  Volume 2, Issue 4, Pages : 661 - 694, 2007

Gabriella Bretti - (email), Ciro D’Apice - (email), Rosanna Manzo - (email), Benedetto Piccoli - (email)

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76

Lyapunov stability analysis of networks of scalar conservation laws

Networks and Heterogeneous Media  Volume 2, Issue 4, Pages : 751 - 759, 2007

Georges Bastin - (email), B. Haut - (email), Jean-Michel Coron - (email), Brigitte d'Andréa-Novel - (email)

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A second order model of road junctions in fluid models of traffic networks

Networks and Heterogeneous Media  Volume 2, Issue 2, Pages : 227 - 253, 2007

Bertrand Haut - (email), Georges Bastin - (email)

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Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes

Networks and Heterogeneous Media  Volume 2, Issue 1, Pages : 127 - 157, 2006

. Adimurthi - (email), Siddhartha Mishra - (email), G.D. Veerappa Gowda - (email)

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Optimal control for continuous supply network models

Networks and Heterogeneous Media  Volume 1, Issue 4, Pages : 675 - 688, 2006

Claus Kirchner - (email), Michael Herty - (email), Simone Göttlich - (email), Axel Klar - (email)

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A fluid dynamic model for supply chains

Networks and Heterogeneous Media  Volume 1, Issue 3, Pages : 379 - 398, 2006

Ciro D'Apice - (email), Rosanna Manzo - (email)

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Optimization criteria for modelling intersections of vehicular traffic flow

Networks and Heterogeneous Media  Volume 1, Issue 2, Pages : 275 - 294, 2006

Michael Herty - (email), S. Moutari - (email), M. Rascle - (email)

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Optimal traffic distribution and priority coefficients for telecommunication networks

Networks and Heterogeneous Media  Volume 1, Issue 2, Pages : 315 - 336, 2006

Alessia Marigo - (email)

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Fast algorithms for the approximation of a traffic flow model on networks

Discrete and Continuous Dynamical Systems - Series B  Volume 6, Issue 3, Pages : 427 - 448, 2006

Gabriella Bretti - (email), Roberto Natalini - (email), Benedetto Piccoli - (email)

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Dynamic parameters identification in traffic flow modeling

DCDS Supplements  Volume 2005, Issue Special, Pages : 190 - 199, 2005

Rinaldo M. Colombo - (email), Andrea Corli - (email)

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85

Traffic circles and timing of traffic lights for cars flow

Discrete and Continuous Dynamical Systems - Series B  Volume 5, Issue 3, Pages : 599 - 630, 2005

Yacine Chitour - (email), Benedetto Piccoli - (email)

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86

The Evans function and stability criteria for degenerate viscous shock waves

Discrete and Continuous Dynamical Systems  Volume 10, Issue 4, Pages : 837 - 855, 2004

Peter Howard - (email), K. Zumbrun - (email)

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Conservation laws and invariant solutions for soil water equations

DCDS Supplements  Volume 2003, Issue Special, Pages : 477 - 481, 2003

C. M. Khalique - (email), G. S. Pai - (email)

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Boundary conditions for multi-dimensional hyperbolic relaxation problems

DCDS Supplements  Volume 2003, Issue Special, Pages : 916 - 925, 2003

Wen-Qing Xu - (email)

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Positivity property of second-order flux-splitting schemes for the compressible Euler equations

Discrete and Continuous Dynamical Systems - Series B  Volume 3, Issue 2, Pages : 201 - 228, 2003

Cheng Wang - (email), Jian-Guo Liu - (email)

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A note on singular limits to hyperbolic systems of conservation laws

Communications on Pure and Applied Analysis  Volume 2, Issue 1, Pages : 51 - 64, 2002

Stefano Bianchini - (email)

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Interaction estimates and Glimm functional for general hyperbolic systems

Discrete and Continuous Dynamical Systems  Volume 9, Issue 1, Pages : 133 - 166, 2002

Stefano Bianchini - (email)

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A center manifold technique for tracing viscous waves

Communications on Pure and Applied Analysis  Volume 1, Issue 2, Pages : 161 - 190, 2002

Stefano Bianchini - (email), Alberto Bressan - (email)

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A uniqueness condition for hyperbolic systems of conservation laws

Discrete and Continuous Dynamical Systems  Volume 6, Issue 3, Pages : 673 - 682, 2000

Alberto Bressan - (email), Marta Lewicka - (email)

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Hyperbolic conservation laws and dynamic systems

Discrete and Continuous Dynamical Systems  Volume 6, Issue 1, Pages : 143 - 145, 1999

Tai-Ping Liu - (email), Shih-Hsien Yu - (email)

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Invariant regions under Lax-Friedrichs scheme for multidimensional systems of conservation laws

Discrete and Continuous Dynamical Systems  Volume 1, Issue 4, Pages : 585 - 593, 1995

Hermano Frid - (email)

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