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Boundary value problem for a phase transition model
1. | Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R. Cozzi 55, 20125 Milano, Italy |
References:
[1] |
D. Amadori, Initial-boundary value problems for nonlinear systems of conservation laws, NoDEA Nonlinear Differential Equations Appl., 4 (1997), 1-42.
doi: 10.1007/PL00001406. |
[2] |
D. Amadori and R. M. Colombo, Continuous dependence for $2\times 2$ conservation laws with boundary, J. Differential Equations, 138 (1997), 229-266.
doi: 10.1006/jdeq.1997.3274. |
[3] |
A. Aw and M. Rascle, Resurrection of "second order'' models of traffic flow, SIAM J. Appl. Math., 60 (2000), 916-938 (electronic).
doi: 10.1137/S0036139997332099. |
[4] |
S. Blandin, D. Work, P. Goatin, B. Piccoli and A. Bayen, A general phase transition model for vehicular traffic, SIAM J. Appl. Math., 71 (2011), 107-127.
doi: 10.1137/090754467. |
[5] |
A. Bressan, Hyperbolic Systems of Conservation Laws, volume 20 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2000. The one-dimensional Cauchy problem. |
[6] |
R. M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math., 63 (2002), 708-721 (electronic).
doi: 10.1137/S0036139901393184. |
[7] |
R. M. Colombo, F. Marcellini and M. Rascle, A 2-phase traffic model based on a speed bound, SIAM J. Appl. Math., 70 (2010), 2652-2666.
doi: 10.1137/090752468. |
[8] |
C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, volume 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, second edition, 2005.
doi: 10.1007/3-540-29089-3. |
[9] |
F. Dubois and P. LeFloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations, 71 (1988), 93-122.
doi: 10.1016/0022-0396(88)90040-X. |
[10] |
M. Garavello and B. Piccoli, Coupling of Lighthill-Whitham-Richards and phase transition models, J. Hyperbolic Differ. Equ., 10 (2013), 577-636.
doi: 10.1142/S0219891613500215. |
[11] |
H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Conservation Laws, volume 152 of Applied Mathematical Sciences, Springer-Verlag, New York, 2002.
doi: 10.1007/978-3-642-56139-9. |
[12] |
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.
doi: 10.1098/rspa.1955.0089. |
[13] |
P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[14] |
H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research Part B, 36 (2002), 275-290.
doi: 10.1016/S0191-2615(00)00050-3. |
show all references
References:
[1] |
D. Amadori, Initial-boundary value problems for nonlinear systems of conservation laws, NoDEA Nonlinear Differential Equations Appl., 4 (1997), 1-42.
doi: 10.1007/PL00001406. |
[2] |
D. Amadori and R. M. Colombo, Continuous dependence for $2\times 2$ conservation laws with boundary, J. Differential Equations, 138 (1997), 229-266.
doi: 10.1006/jdeq.1997.3274. |
[3] |
A. Aw and M. Rascle, Resurrection of "second order'' models of traffic flow, SIAM J. Appl. Math., 60 (2000), 916-938 (electronic).
doi: 10.1137/S0036139997332099. |
[4] |
S. Blandin, D. Work, P. Goatin, B. Piccoli and A. Bayen, A general phase transition model for vehicular traffic, SIAM J. Appl. Math., 71 (2011), 107-127.
doi: 10.1137/090754467. |
[5] |
A. Bressan, Hyperbolic Systems of Conservation Laws, volume 20 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2000. The one-dimensional Cauchy problem. |
[6] |
R. M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math., 63 (2002), 708-721 (electronic).
doi: 10.1137/S0036139901393184. |
[7] |
R. M. Colombo, F. Marcellini and M. Rascle, A 2-phase traffic model based on a speed bound, SIAM J. Appl. Math., 70 (2010), 2652-2666.
doi: 10.1137/090752468. |
[8] |
C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, volume 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, second edition, 2005.
doi: 10.1007/3-540-29089-3. |
[9] |
F. Dubois and P. LeFloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations, 71 (1988), 93-122.
doi: 10.1016/0022-0396(88)90040-X. |
[10] |
M. Garavello and B. Piccoli, Coupling of Lighthill-Whitham-Richards and phase transition models, J. Hyperbolic Differ. Equ., 10 (2013), 577-636.
doi: 10.1142/S0219891613500215. |
[11] |
H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Conservation Laws, volume 152 of Applied Mathematical Sciences, Springer-Verlag, New York, 2002.
doi: 10.1007/978-3-642-56139-9. |
[12] |
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.
doi: 10.1098/rspa.1955.0089. |
[13] |
P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[14] |
H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research Part B, 36 (2002), 275-290.
doi: 10.1016/S0191-2615(00)00050-3. |
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