-
1
-
-
0033691480
-
-
A. AW and M. RASCLE, Resurrection of second order models of traffic flow, SLAM J. Appl. Math. 60 (2000), 916-938 (electronic), http://dx.doi.org/10.1137/S0036139997332099. MR 1750085 (2001a:35111)
-
A. AW and M. RASCLE, Resurrection of "second order" models of traffic flow, SLAM J. Appl. Math. 60 (2000), 916-938 (electronic), http://dx.doi.org/10.1137/S0036139997332099. MR 1750085 (2001a:35111)
-
-
-
-
2
-
-
26344440071
-
-
M. BANDO, K. HASEBE, A. NAKAYAMA, A. SHIBATA, and Y. SUGIYAMA, Dynamical model of traffic congestion and numerical simulations (1995), 1035-1042, http://dx.doi.org/ 10.1103/PhysRevE.51.1035.
-
(1995)
Dynamical model of traffic congestion and numerical simulations
, pp. 1035-1042
-
-
BANDO, M.1
HASEBE, K.2
NAKAYAMA, A.3
SHIBATA, A.4
SUGIYAMA, Y.5
-
3
-
-
84990689276
-
Hyperbolic conservation laws with stiff relaxation terms and entropy
-
95h:35133
-
G. Q. CHEN, C. D. LEVERMORE, and T. P. LIU, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 47 (1994), 787-830, http://dx.doi.org/10.1002/cpa. 3160470602. MR 1280989 (95h:35133)
-
(1994)
Comm. Pure Appl. Math
, vol.47
, pp. 787-830
-
-
CHEN, G.Q.1
LEVERMORE, C.D.2
LIU, T.P.3
-
4
-
-
84875094914
-
-
R. COURANT and D. HILBERT, Methods of Mathematical Physics. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391 (16,426a)
-
R. COURANT and D. HILBERT, Methods of Mathematical Physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391 (16,426a)
-
-
-
-
5
-
-
0000824680
-
Hyperbolic systems and balance laws with inhomogeneity and dissipation
-
83m:35093
-
C. M. DAFERMOS and L. HSIAO, Hyperbolic systems and balance laws with inhomogeneity and dissipation, Indiana Univ. Math. J. 31 (1982), 471-491, http://dx.doi.org/10.1512/iumj.1982.31.31039. MR 662914 (83m:35093)
-
(1982)
Indiana Univ. Math. J
, vol.31
, pp. 471-491
-
-
DAFERMOS, C.M.1
HSIAO, L.2
-
6
-
-
84980073473
-
Some existence theorems for hyperbolic systems of partial differential equations in two independent variables
-
14,655a
-
A. DOUGLIS, Some existence theorems for hyperbolic systems of partial differential equations in two independent variables, Comm. Pure Appl. Math. 5 (1952), 119-154, http://dx.doi.org/10.1002/cpa.3160050202. MR 0052666 (14,655a)
-
(1952)
Comm. Pure Appl. Math
, vol.5
, pp. 119-154
-
-
DOUGLIS, A.1
-
7
-
-
0013184506
-
-
S. ENGELBERG, H. L. LIU, and E. TADMOR, Critical thresholds in Euler-Poisson equations, Indiana Univ. Math. J. 50 (2001), 109-157, Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000). MR 1855666 (2002i:35149)
-
S. ENGELBERG, H. L. LIU, and E. TADMOR, Critical thresholds in Euler-Poisson equations, Indiana Univ. Math. J. 50 (2001), 109-157, Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000). MR 1855666 (2002i:35149)
-
-
-
-
8
-
-
0002810672
-
An analysis of traffic flow
-
MR 0101166 20 #7588
-
H. GREENBERG, An analysis of traffic flow, Operations Res. 7 (1959), 79-85. MR 0101166 (20 #7588)
-
(1959)
Operations Res
, vol.7
, pp. 79-85
-
-
GREENBERG, H.1
-
9
-
-
0036306864
-
-
J. M. GREENBERG, Extensions and amplifications of a traffic model of Aw and Rascle, SIAM J. Appl. Math. 62 (2001/02), 729-745 (electronic), http://dx.doi.org/10.1137/S0036139900378657. MR 1897720 (2003b:90018)
-
J. M. GREENBERG, Extensions and amplifications of a traffic model of Aw and Rascle, SIAM J. Appl. Math. 62 (2001/02), 729-745 (electronic), http://dx.doi.org/10.1137/S0036139900378657. MR 1897720 (2003b:90018)
-
-
-
-
11
-
-
0000364772
-
On hyperbolic partial differential equations
-
14,475a
-
P. HARTMAN and A. WINTNER, On hyperbolic partial differential equations, Amer. J. Math. 74 (1952), 834-864, http://dx.doi.org/10.2307/2372229. MR 0051413 (14,475a)
-
(1952)
Amer. J. Math
, vol.74
, pp. 834-864
-
-
HARTMAN, P.1
WINTNER, A.2
-
12
-
-
0035470907
-
Traffic and related self-driven many-particle systems
-
D. HELBING, Traffic and related self-driven many-particle systems, Rev. Modern Phy. 73 (2001), 1067-1141, http://dx.doi.org/10. 1103/RevModPhys.73.1067.
-
(2001)
Rev. Modern Phy
, vol.73
, pp. 1067-1141
-
-
HELBING, D.1
-
13
-
-
84990701264
-
The relaxation schemes for systems of conservation laws in arbitrary space dimensions
-
96c:65134
-
S. JIN and Z. P. XIN, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995), 235-276, http://dx.doi.org/10.1002/cpa.3160480303. MR 1322811 (96c:65134)
-
(1995)
Comm. Pure Appl. Math
, vol.48
, pp. 235-276
-
-
JIN, S.1
XIN, Z.P.2
-
14
-
-
0002562202
-
Structure and parameters of clusters in traffic flow
-
B. S. KERNER and P. KONHÄUSER, Structure and parameters of clusters in traffic flow, Physical Review E 50 (1994), 54-83, http://dx.doi.org/10.1103/PhysRevE.50.54.
-
(1994)
Physical Review E
, vol.50
, pp. 54-83
-
-
KERNER, B.S.1
KONHÄUSER, P.2
-
15
-
-
84980192441
-
Formation of singularities in one-dimensional nonlinear wave propagation
-
MR 0369934 51 #6163
-
F. JOHN, Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math. 27 (1974), 377-405. MR 0369934 (51 #6163)
-
(1974)
Comm. Pure Appl. Math
, vol.27
, pp. 377-405
-
-
JOHN, F.1
-
16
-
-
0031581268
-
The zero relaxation limit for the hydrody namic Whitham traffic flow model
-
98j:35118
-
C. LATTANZIO and P. MARCATI The zero relaxation limit for the hydrody namic Whitham traffic flow model, J. Differential Equations 141 (1997), 150-178, http://dx.doi.org/10.1006/jdeq.1997.3311. MR 1485946 (98j:35118)
-
(1997)
J. Differential Equations
, vol.141
, pp. 150-178
-
-
LATTANZIO, C.1
MARCATI, P.2
-
17
-
-
33750483511
-
Development of singularities of solutions of nonlinear hyperbolic partial differential equations
-
29 #2532
-
P. D. LAX, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Mathematical Phys. 5 (1964), 611-613, http://dx.doi.org/10.1063/1.1704154. MR 0165243 (29 #2532)
-
(1964)
J. Mathematical Phys
, vol.5
, pp. 611-613
-
-
LAX, P.D.1
-
18
-
-
0034923773
-
-
T. LI, Global solutions and zero relaxation limit for a traffic flow model, SIAM J. Appl. Math. 61 (2000), 1042-1061 (electronic), http://dx.doi.org/10.1137/S0036139999356788. MR 1788029 (2002i:35122)
-
T. LI, Global solutions and zero relaxation limit for a traffic flow model, SIAM J. Appl. Math. 61 (2000), 1042-1061 (electronic), http://dx.doi.org/10.1137/S0036139999356788. MR 1788029 (2002i:35122)
-
-
-
-
19
-
-
52549124639
-
-
1 stability of conservation laws for a traffic flow model, Electron. J. Differential Equations (2001), No. 14, 18 pp. (electronic). MR 1811787 (2001m:35214)
-
1 stability of conservation laws for a traffic flow model, Electron. J. Differential Equations (2001), No. 14, 18 pp. (electronic). MR 1811787 (2001m:35214)
-
-
-
-
20
-
-
0038367810
-
Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow, J
-
10.1016/S0022-0396(03)00014-7. MR 1970959 2004a:35153
-
Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow, J. Differential Equations 190 (2003), 131-149, http://dx.doi.org/10.1016/S0022-0396(03)00014-7. MR 1970959 (2004a:35153)
-
(2003)
Differential Equations
, vol.190
, pp. 131-149
-
-
-
21
-
-
20744454119
-
-
Nonlinear dynamics of traffic jams, Phys. D 207 (2005), 41-51, http://dx.doi.org/10.1016/j.physd.2005.05.011. MR 2166973 (2006c:35022)
-
Nonlinear dynamics of traffic jams, Phys. D 207 (2005), 41-51, http://dx.doi.org/10.1016/j.physd.2005.05.011. MR 2166973 (2006c:35022)
-
-
-
-
22
-
-
84875122602
-
-
T. LI and H. L. LIU, Stability of a traffic flow model with nonconvex relaxation, Commun. Math. Sci. 3 (2005), 101-118. MR 2164192 (2006b:35217)
-
T. LI and H. L. LIU, Stability of a traffic flow model with nonconvex relaxation, Commun. Math. Sci. 3 (2005), 101-118. MR 2164192 (2006b:35217)
-
-
-
-
24
-
-
33748421771
-
-
H. L. LIU, Wave breaking in a class of nonlocal dispersive wave equations, J. Nonlinear Math. Phys. 13 (2006), 441-466, http://dx.doi.org/10.2991/jnmp.2006.13.3.8. MR 2249812 (2007i:35203)
-
H. L. LIU, Wave breaking in a class of nonlocal dispersive wave equations, J. Nonlinear Math. Phys. 13 (2006), 441-466, http://dx.doi.org/10.2991/jnmp.2006.13.3.8. MR 2249812 (2007i:35203)
-
-
-
-
25
-
-
29344463413
-
-
Critical thresholds in the semiclassical limit of 2-D rotational Schrödinger equations, Z. Angew. Math. Phys. 57 (2006), 42-58. MR 2196753 (2006m:35303)
-
Critical thresholds in the semiclassical limit of 2-D rotational Schrödinger equations, Z. Angew. Math. Phys. 57 (2006), 42-58. MR 2196753 (2006m:35303)
-
-
-
-
26
-
-
84875111892
-
-
Relaxation dynamics, scaling limits and convergence of relaxation schemes, Analysis and Numerics for Conservation Laws, Springer, Berlin, 2005, pp. 453-478. MR 2169940 (2006i:65124)
-
Relaxation dynamics, scaling limits and convergence of relaxation schemes, Analysis and Numerics for Conservation Laws, Springer, Berlin, 2005, pp. 453-478. MR 2169940 (2006i:65124)
-
-
-
-
27
-
-
0042157210
-
Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws, J
-
10.1016/S0022-0396(03)00124-4. MR 1990842 2004d:35165
-
Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws, J. Differential Equations 192 (2003), 285-307, http://dx.doi.org/10.1016/S0022-0396(03)00124-4. MR 1990842 (2004d:35165)
-
(2003)
Differential Equations
, vol.192
, pp. 285-307
-
-
-
28
-
-
0035556990
-
-
H. L. LIU and E. TADMOR, Critical thresholds in a convolution model for nonlinear conservation laws, SIAM J. Math. Anal. 33 (2001), 930-945 (electronic), http://dx.doi.org/10.1137/ S0036141001386908. MR 1885290 (2003j:35210)
-
H. L. LIU and E. TADMOR, Critical thresholds in a convolution model for nonlinear conservation laws, SIAM J. Math. Anal. 33 (2001), 930-945 (electronic), http://dx.doi.org/10.1137/ S0036141001386908. MR 1885290 (2003j:35210)
-
-
-
-
31
-
-
1642544667
-
-
H. LIU and E. TADMOR, Critical thresholds in 2D restricted Euler-Poisson equations, SIAM J. Appl. Math. 63 (2003), 1889-1910 (electronic), http://dx.doi.org/10.1137/S0036139902416986. MR 2030849 (2005g:35245)
-
H. LIU and E. TADMOR, Critical thresholds in 2D restricted Euler-Poisson equations, SIAM J. Appl. Math. 63 (2003), 1889-1910 (electronic), http://dx.doi.org/10.1137/S0036139902416986. MR 2030849 (2005g:35245)
-
-
-
-
32
-
-
0347270355
-
-
H. L. LIU and E. TADMOR, Rotation prevents finite-time breakdown, Phys. D 188 (2004), 262-276, http://dx.doi.org/10.1016/j.physd.2003.07.006. MR 2043732 (2005a:76161)
-
H. L. LIU and E. TADMOR, Rotation prevents finite-time breakdown, Phys. D 188 (2004), 262-276, http://dx.doi.org/10.1016/j.physd.2003.07.006. MR 2043732 (2005a:76161)
-
-
-
-
33
-
-
0002990049
-
Development of singularities in the nonlinear waves for quasilinear hyperbolic partial differential equations
-
http://dx.doi.org/10.1016/0022- 0396(79)90082-2. MR 540819 80g:35075
-
T. P. LIU, Development of singularities in the nonlinear waves for quasilinear hyperbolic partial differential equations, J. Differential Equations 33 (1979), 92-111, http://dx.doi.org/10.1016/0022- 0396(79)90082-2. MR 540819 (80g:35075)
-
(1979)
J. Differential Equations
, vol.33
, pp. 92-111
-
-
LIU, T.P.1
-
34
-
-
21544449601
-
Hyperbolic conservation laws with relaxation
-
88f:5092
-
Hyperbolic conservation laws with relaxation, Comm. Math. Phys. 108 (1987), 153-175, http://dx.doi.org/10.1007/BF01210707. MR 872145 (88f:5092)
-
(1987)
Comm. Math. Phys
, vol.108
, pp. 153-175
-
-
-
35
-
-
0013040387
-
-
C. MASCIA and K. ZUMBRUN, Pointwise Green's function bounds and stability of relaxation shocks, Indiana Univ. Math. J. 51 (2002), 773-904, http://dx.doi.org/10.1512/iumj.2002.51.2212. MR 1947862 (2003k:35151)
-
C. MASCIA and K. ZUMBRUN, Pointwise Green's function bounds and stability of relaxation shocks, Indiana Univ. Math. J. 51 (2002), 773-904, http://dx.doi.org/10.1512/iumj.2002.51.2212. MR 1947862 (2003k:35151)
-
-
-
-
36
-
-
33646598368
-
-
Stability of large-amplitude shock profiles of general relaxation systems, SIAM J. Math. Anal. 37 (2005), 889-913 (electronic), http://dx.doi.org/10.1137/S0036141004435844. MR 2191781 (2006j:35151)
-
Stability of large-amplitude shock profiles of general relaxation systems, SIAM J. Math. Anal. 37 (2005), 889-913 (electronic), http://dx.doi.org/10.1137/S0036141004435844. MR 2191781 (2006j:35151)
-
-
-
-
37
-
-
49349105883
-
-
Publications Mathématiques d'Orsay, 02, Département de Mathématique, Université de Paris-Sud, Orsay, MR 0481578 58 #1690
-
T. NISHIDA, Nonlinear Hyperbolic Equations and Related Topics in Fluid dynamics, Publications Mathématiques d'Orsay, vol. 78-02, Département de Mathématique, Université de Paris-Sud, Orsay, 1978. MR 0481578 (58 #1690)
-
(1978)
Nonlinear Hyperbolic Equations and Related Topics in Fluid dynamics
, vol.78
-
-
NISHIDA, T.1
-
38
-
-
84875093655
-
-
H. J. PAYNE, Models of freeway traffic and control, Simulation Councils Proc. (G. A. Bekey, ed.), Mathematical Models of Public Systems, 1, La Jolla, CA, 1971, pp. 51-61.
-
H. J. PAYNE, Models of freeway traffic and control, Simulation Councils Proc. (G. A. Bekey, ed.), Mathematical Models of Public Systems, vol. 1, La Jolla, CA, 1971, pp. 51-61.
-
-
-
-
40
-
-
0002499554
-
Formation of singularities in compressible Euler-Poisson fluids with heat diffusion and damping relaxation
-
99b:35178
-
D. WANG and G.-Q. CHEN, Formation of singularities in compressible Euler-Poisson fluids with heat diffusion and damping relaxation, J. Differential Equations 144 (1998), 44-65, http://dx.doi.org/10.1006/jdeq.1997.3377. MR 1615127 (99b:35178)
-
(1998)
J. Differential Equations
, vol.144
, pp. 44-65
-
-
WANG, D.1
CHEN, G.-Q.2
-
41
-
-
0004181419
-
-
Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons, New York, MR 0483954 58 #3905
-
G. B. WHITHAM, Linear and Nonlinear Waves, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1974. MR 0483954 (58 #3905)
-
(1974)
Linear and Nonlinear Waves
-
-
WHITHAM, G.B.1
-
42
-
-
0032158275
-
A theory of nonequilibrium traffic flow
-
http://dx.doi.org/10. 1016/S0191-2615(98)00014-9
-
H. M. ZHANG, A theory of nonequilibrium traffic flow, Transportation Research, B. 32 (7) (1998), 485-498, http://dx.doi.org/10. 1016/S0191-2615(98)00014-9.
-
(1998)
Transportation Research, B
, vol.32
, Issue.7
, pp. 485-498
-
-
ZHANG, H.M.1
|