Global well posedness of traffic flow models with phase transitions

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 11, 2007, Pages 2413-2426

  Colombo, Rinaldo M ^a   Goatin, Paola ^b   Priuli, Fabio S ^c  

^a Department of Mathematics ^*  (Italy)

^b UNIVERSITÉ DE TOULON   (France)

^c SISSA   (Italy)

Author keywords

Continuum traffic models; Hyperbolic conservation laws; Phase transitions

Indexed keywords

FLOW OF FLUIDS; PHASE TRANSITIONS; PROBLEM SOLVING;

CAUCHY PROBLEM; CONTINUUM TRAFFIC MODELS; HYPERBOLIC CONSERVATION LAWS;

CONTINUUM MECHANICS;

EID: 33847370265     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.03.029     Document Type: Article

References (24)

1. Amadori D., and Colombo R.M. Continuous dependence for 2×2 conservation laws with boundary. J. Differential Equations 138 2 (1997) 229-266
2. Amadori D., and Colombo R.M. Viscosity solutions and standard Riemann semigroup for conservation laws with boundary. Rend. Sem. Mat. Univ. Padova 99 (1998) 219-245
3. Bianchini S. The semigroup generated by a Temple class system with non-convex flux function. Differential Integral Equations 13 10-12 (2000) 1529-1550
4. Bressan A. Hyperbolic Systems of Conservation Laws (2000), Oxford University Press
5. Bressan A., and Colombo R.M. The semigroup generated by 2×2 conservation laws. Arch. Ration. Mech. Anal. 133 1 (1995) 1-75
6. Colombo R.M. A 2×2 hyperbolic traffic flow model. Math. Comput. Modeling 35 5-6 (2002) 683-688 Traffic flow-modeling and simulation
7. Colombo R.M. Hyperbolic phase transitions in traffic flow. SIAM J. Appl. Math. 63 2 (2002) 708-721
8. Colombo R.M., and Corli A. Continuous dependence in conservation laws with phase transitions. SIAM J. Math. Anal. 31 1 (1999) 34-62
9. Colombo R.M., and Corli A. Sonic hyperbolic phase transitions and Chapman-Jouguet detonations. J. Differential Equations 184 2 (2002) 321-347
10. Colombo R.M., and Corli A. On a class of hyperbolic balance laws. J. Hyperbolic Differ. Equ. 1 4 (2004) 725-745
11. Colombo R.M., and Groli A. Minimising stop and go waves to optimise traffic flow. Appl. Math. Lett. 17 6 (2004) 697-701
12. Colombo R.M., and Groli A. On the initial boundary value problem for Temple systems. Nonlinear Anal. 56 4 (2004) 569-589
13. Colombo R.M., and Priuli F.S. Characterization of Riemann solvers for the two phase p-system. Comm. Partial Differential Equations 28 7-8 (2003) 1371-1390
14. Colombo R.M., and Rosini M.D. Well posedness of balance laws with boundary. J. Math. Anal. Appl., 0022-247X 311 2 (2005) 683-702
15. Dafermos C.M. Hyperbolic Conservation Laws in Continuum Physics. 1st edition (2000), Springer-Verlag, New York
16. Drake J.S., Schofer J.L., and May A.D. A statistical Analysis of Speed Density Hypothesis. Highway Research Record vol. 154 (1967) 53-87
17. Edie L.C. Car following and steady-state theory for non-congested traffic. Oper. Res. 9 (1961) 66-76
18. J. Goodman, Initial boundary value problems for hyperbolic systems of conservation laws, Ph.D. Thesis, California University, 1982
19. Lefloch P.G., and Thanh M.D. Nonclassical Riemann solvers and kinetic relations. I. A nonconvex hyperbolic model of phase transitions. Z. Angew. Math. Phys. 52 4 (2001) 597-619
20. Lefloch P.G., and Thanh M.D. Non-classical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase-transition dynamics. Proc. Roy. Soc. Edinburgh Sect. A 132 1 (2002) 181-219
21. Lighthill M.J., and Whitham G.B. On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A. 229 (1955) 317-345
22. Newell G.F. A simplified car-following theory: a lower order model. Transport. Res. B 36 3 (2002) 195-205
23. Richards P.I. Shock waves on the highway. Oper. Res. 4 (1956) 42-51
24. Zhang H.M., and Kim T. A car-following theory for multiphase vehicular traffic flow. Transport. Res. B 39 5 (2005) 385-399