-
Previous Article
Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes
- DCDS Home
- This Issue
- Next Article
The Cauchy problem at a node with buffer
1. | Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale “A. Avogadro”, viale T. Michel 11, 15121 Alessandria, Italy |
2. | INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex, France |
References:
[1] |
M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks, Netw. Heterog. Media, 1 (2006), 41-56 (electronic). |
[2] |
A. Bressan, A contractive metric for systems of conservation laws with coinciding shock and rarefaction curves, J. Differential Equations, 106 (1993), 332-366.
doi: 10.1006/jdeq.1993.1111. |
[3] |
A. Bressan, "Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem," Oxford Lecture Series in Mathematics and its Applications, 20, Oxford University Press, Oxford, 2000. |
[4] |
A. Bressan and R. M. Colombo, The semigroup generated by $2\times 2$ conservation laws, Arch. Rational Mech. Anal., 133 (1995), 1-75.
doi: 10.1007/BF00375350. |
[5] |
A. Bressan, G. Crasta and B. Piccoli, Well-posedness of the Cauchy problem for $n\times n$ systems of conservation laws, Mem. Amer. Math. Soc., 146 (2000), viii+134 pp. |
[6] |
G. M. Coclite, M. Garavello and B. Piccoli, Traffic flow on a road network, SIAM J. Math. Anal., 36 (2005), 1862-1886 (electronic).
doi: 10.1137/S0036141004402683. |
[7] |
R. M. Colombo, P. Goatin and B. Piccoli, Road network with phase transitions, J. Hyperbolic Differ. Equ., 7 (2010), 85-106.
doi: 10.1142/S0219891610002025. |
[8] |
C. D'apice, R. Manzo and B. Piccoli, Packet flow on telecommunication networks, SIAM J. Math. Anal., 38 (2006), 717-740 (electronic).
doi: 10.1137/050631628. |
[9] |
M. Garavello and B. Piccoli, Traffic flow on a road network using the Aw-Rascle model, Comm. Partial Differential Equations, 31 (2006), 243-275. |
[10] |
M. Garavello and B. Piccoli, "Traffic Flow on Networks. Conservation Laws Models," AIMS Series on Applied Mathematics, 1, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2006. |
[11] |
M. Garavello and B. Piccoli, Conservation laws on complex networks, Ann. H. Poincaré, 26 (2009), 1925-1951. |
[12] |
M. Garavello and B. Piccoli, A multibuffer model for LWR road networks, preprint, 2010. |
[13] |
S. Göttlich, M. Herty and A. Klar, Modelling and optimization of supply chains on complex networks, Commun. Math. Sci., 4 (2006), 315-330. |
[14] |
M. Herty, A. Klar and B. Piccoli, Existence of solutions for supply chain models based on partial differential equations, SIAM J. Math. Anal., 39 (2007), 160-173.
doi: 10.1137/060659478. |
[15] |
M. Herty, J.-P. Lebacque and S. Moutari, A novel model for intersections of vehicular traffic flow, Netw. Heterog. Media, 4 (2009), 813-826 (electronic). |
[16] |
M. Herty, S. Moutari and M. Rascle, Optimization criteria for modelling intersections of vehicular traffic flow, Netw. Heterog. Media, 1 (2006), 275-294 (electronic).
doi: 10.3934/nhm.2006.1.275. |
[17] |
M. Herty and M. Rascle, Coupling conditions for a class of second-order models for traffic flow, SIAM J. Math. Anal., 38 (2006), 595-616.
doi: 10.1137/05062617X. |
[18] |
H. Holden and N. H. Risebro, "Front Tracking for Hyperbolic Conservation Laws," Applied Mathematical Sciences, 152, Springer-Verlag, New York, 2002. |
[19] |
M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London. Ser. A., 229 (1955), 317-345. |
[20] |
A. Marigo and B. Piccoli, A fluid dynamic model for $T$-junctions, SIAM J. Math. Anal., 39 (2008), 2016-2032.
doi: 10.1137/060673060. |
[21] |
P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[22] |
D. Sun, I. S. Strub and A. M. Bayen, Comparison of the performance of four Eulerian network flow models for strategic air traffic management, Netw. Heterog. Media, 2 (2007), 569-595.
doi: 10.3934/nhm.2007.2.569. |
show all references
References:
[1] |
M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks, Netw. Heterog. Media, 1 (2006), 41-56 (electronic). |
[2] |
A. Bressan, A contractive metric for systems of conservation laws with coinciding shock and rarefaction curves, J. Differential Equations, 106 (1993), 332-366.
doi: 10.1006/jdeq.1993.1111. |
[3] |
A. Bressan, "Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem," Oxford Lecture Series in Mathematics and its Applications, 20, Oxford University Press, Oxford, 2000. |
[4] |
A. Bressan and R. M. Colombo, The semigroup generated by $2\times 2$ conservation laws, Arch. Rational Mech. Anal., 133 (1995), 1-75.
doi: 10.1007/BF00375350. |
[5] |
A. Bressan, G. Crasta and B. Piccoli, Well-posedness of the Cauchy problem for $n\times n$ systems of conservation laws, Mem. Amer. Math. Soc., 146 (2000), viii+134 pp. |
[6] |
G. M. Coclite, M. Garavello and B. Piccoli, Traffic flow on a road network, SIAM J. Math. Anal., 36 (2005), 1862-1886 (electronic).
doi: 10.1137/S0036141004402683. |
[7] |
R. M. Colombo, P. Goatin and B. Piccoli, Road network with phase transitions, J. Hyperbolic Differ. Equ., 7 (2010), 85-106.
doi: 10.1142/S0219891610002025. |
[8] |
C. D'apice, R. Manzo and B. Piccoli, Packet flow on telecommunication networks, SIAM J. Math. Anal., 38 (2006), 717-740 (electronic).
doi: 10.1137/050631628. |
[9] |
M. Garavello and B. Piccoli, Traffic flow on a road network using the Aw-Rascle model, Comm. Partial Differential Equations, 31 (2006), 243-275. |
[10] |
M. Garavello and B. Piccoli, "Traffic Flow on Networks. Conservation Laws Models," AIMS Series on Applied Mathematics, 1, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2006. |
[11] |
M. Garavello and B. Piccoli, Conservation laws on complex networks, Ann. H. Poincaré, 26 (2009), 1925-1951. |
[12] |
M. Garavello and B. Piccoli, A multibuffer model for LWR road networks, preprint, 2010. |
[13] |
S. Göttlich, M. Herty and A. Klar, Modelling and optimization of supply chains on complex networks, Commun. Math. Sci., 4 (2006), 315-330. |
[14] |
M. Herty, A. Klar and B. Piccoli, Existence of solutions for supply chain models based on partial differential equations, SIAM J. Math. Anal., 39 (2007), 160-173.
doi: 10.1137/060659478. |
[15] |
M. Herty, J.-P. Lebacque and S. Moutari, A novel model for intersections of vehicular traffic flow, Netw. Heterog. Media, 4 (2009), 813-826 (electronic). |
[16] |
M. Herty, S. Moutari and M. Rascle, Optimization criteria for modelling intersections of vehicular traffic flow, Netw. Heterog. Media, 1 (2006), 275-294 (electronic).
doi: 10.3934/nhm.2006.1.275. |
[17] |
M. Herty and M. Rascle, Coupling conditions for a class of second-order models for traffic flow, SIAM J. Math. Anal., 38 (2006), 595-616.
doi: 10.1137/05062617X. |
[18] |
H. Holden and N. H. Risebro, "Front Tracking for Hyperbolic Conservation Laws," Applied Mathematical Sciences, 152, Springer-Verlag, New York, 2002. |
[19] |
M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London. Ser. A., 229 (1955), 317-345. |
[20] |
A. Marigo and B. Piccoli, A fluid dynamic model for $T$-junctions, SIAM J. Math. Anal., 39 (2008), 2016-2032.
doi: 10.1137/060673060. |
[21] |
P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[22] |
D. Sun, I. S. Strub and A. M. Bayen, Comparison of the performance of four Eulerian network flow models for strategic air traffic management, Netw. Heterog. Media, 2 (2007), 569-595.
doi: 10.3934/nhm.2007.2.569. |
[1] |
Paola Goatin, Elena Rossi. Comparative study of macroscopic traffic flow models at road junctions. Networks and Heterogeneous Media, 2020, 15 (2) : 261-279. doi: 10.3934/nhm.2020012 |
[2] |
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 |
[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] |
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 |
[5] |
Michael Herty, Reinhard Illner. Analytical and numerical investigations of refined macroscopic traffic flow models. Kinetic and Related Models, 2010, 3 (2) : 311-333. doi: 10.3934/krm.2010.3.311 |
[6] |
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 |
[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] |
Bertrand Haut, Georges Bastin. A second order model of road junctions in fluid models of traffic networks. Networks and Heterogeneous Media, 2007, 2 (2) : 227-253. doi: 10.3934/nhm.2007.2.227 |
[10] |
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 |
[11] |
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 |
[12] |
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 |
[13] |
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 |
[14] |
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 |
[15] |
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 |
[16] |
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 |
[17] |
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 |
[18] |
Markus Musch, Ulrik Skre Fjordholm, Nils Henrik Risebro. Well-posedness theory for nonlinear scalar conservation laws on networks. Networks and Heterogeneous Media, 2022, 17 (1) : 101-128. doi: 10.3934/nhm.2021025 |
[19] |
Alexander Bobylev, Mirela Vinerean, Åsa Windfäll. Discrete velocity models of the Boltzmann equation and conservation laws. Kinetic and Related Models, 2010, 3 (1) : 35-58. doi: 10.3934/krm.2010.3.35 |
[20] |
Marte Godvik, Harald Hanche-Olsen. Car-following and the macroscopic Aw-Rascle traffic flow model. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 279-303. doi: 10.3934/dcdsb.2010.13.279 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]