메뉴 건너뛰기




Volumn 35, Issue 4, 2004, Pages 949-973

A multiclass homogenized hyperbolic model of traffic flow

Author keywords

Discontinuous flux; Homogenization; Hydrodynamic limit; Hyperbolic systems of conservation laws; Multiclass models; Traffic flow; Uniqueness

Indexed keywords


EID: 3142655881     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141002411490     Document Type: Article
Times cited : (48)

References (49)
  • 1
    • 0033691480 scopus 로고    scopus 로고
    • Resurrection of "second order" models of traffic flow
    • A. Aw AND M. RASCLE, Resurrection of "second order" models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916-938.
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 916-938
    • Aw, A.1    Rascle, M.2
  • 2
    • 0036706213 scopus 로고    scopus 로고
    • Derivation of continuum traffic flow models from microscopic follow-the-leader models
    • A. Aw, A. KLAR, T. MATERNE, AND M. RASCLE, Derivation of continuum traffic flow models from microscopic follow-the-leader models SIAM J. Appl. Math., 63 (2002), pp. 259-278.
    • (2002) SIAM J. Appl. Math. , vol.63 , pp. 259-278
    • Aw, A.1    Klar, A.2    Materne, T.3    Rascle, M.4
  • 3
    • 0000865261 scopus 로고    scopus 로고
    • The semigroup generated by a temple class system with large data
    • P. HAITI AND A. BRESSAN, The semigroup generated by a temple class system with large data, Differential Integral Equations, 10 (1997), pp. 401-418.
    • (1997) Differential Integral Equations , vol.10 , pp. 401-418
    • Haiti, P.1    Bressan, A.2
  • 5
    • 0000093666 scopus 로고
    • A version of the fundamental theorem for Young measures
    • PDEs and Continuum Models of Phase Transitions, M. Rascle, D. Serre, and M. Slemrod, eds., Springer-Verlag, Berlin
    • J. M. BALL, A version of the fundamental theorem for Young measures, in PDEs and Continuum Models of Phase Transitions, Lecture Notes in Phys. 344, M. Rascle, D. Serre, and M. Slemrod, eds., Springer-Verlag, Berlin, 1989, pp. 207-215.
    • (1989) Lecture Notes in Phys. , vol.344 , pp. 207-215
    • Ball, J.M.1
  • 6
    • 3142737528 scopus 로고    scopus 로고
    • An n-populations model for traffic flow
    • preprint, or http://dm.ing.unibs.it/rinaldo/, to appear
    • S. BENZONI-GAVAGE AND R. M. COLOMBO, An n-Populations Model for Traffic Flow, preprint, http://www.umpa.ens-lyon.fr/~benzonil/ or http://dm.ing.unibs. it/rinaldo/, 2002; European J. Appl. Math., to appear.
    • (2002) European J. Appl. Math.
    • Benzoni-Gavage, S.1    Colombo, R.M.2
  • 7
    • 0000229008 scopus 로고
    • Intégrandes normales et mesures paramétrées en calcul des variations
    • H. BERLIOCCHI AND J.-M. LASRY, Intégrandes normales et mesures paramétrées en calcul des variations, Bull. Soc. Math. Prance, 101 (1973), pp. 129-184.
    • (1973) Bull. Soc. Math. Prance , vol.101 , pp. 129-184
    • Berliocchi, H.1    Lasry, J.-M.2
  • 8
    • 0001096844 scopus 로고    scopus 로고
    • The semigroup generated by a Temple class system with non-convex flux function
    • S. BIANCHINI, The semigroup generated by a Temple class system with non-convex flux function, Differential Integral Equations, 13 (2000), pp. 1529-1550.
    • (2000) Differential Integral Equations , vol.13 , pp. 1529-1550
    • Bianchini, S.1
  • 9
    • 0035555621 scopus 로고    scopus 로고
    • infin solutions for hyperbolic systems with coinciding shocks and rarefactions
    • infin solutions for hyperbolic systems with coinciding shocks and rarefactions, SIAM J. Math. Anal., 33 (2001), pp. 959-981.
    • (2001) SIAM J. Math. Anal. , vol.33 , pp. 959-981
    • Bianchini, S.1
  • 10
    • 3142705348 scopus 로고
    • Propagation des oscillations dans deux classes de systèmes hyperboliques (2 × 2 et 3 × 3)
    • M. BONNEFILLE, Propagation des oscillations dans deux classes de systèmes hyperboliques (2 × 2 et 3 × 3), Comm. Partial Differential Equations, 13 (1988), pp. 905-925.
    • (1988) Comm. Partial Differential Equations , vol.13 , pp. 905-925
    • Bonnefille, M.1
  • 14
    • 84990576544 scopus 로고
    • Propagation and cancellation of oscillations for hyperbolic systems of conservation laws
    • G.-Q. CHEN, Propagation and cancellation of oscillations for hyperbolic systems of conservation laws, Comm. Pure Appl. Math., 44 (1991), pp. 121-140.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 121-140
    • Chen, G.-Q.1
  • 17
    • 10444283684 scopus 로고    scopus 로고
    • A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections
    • Univeristy of California Berkeley, Berkeley, CA
    • C. F. DAGANZO, A Behavioral Theory of Multi-lane Traffic Flow. Part I: Long Homogeneous Freeway Sections, Research report UCB-ITS-RR 99-5, Univeristy of California Berkeley, Berkeley, CA, 2002.
    • (2002) Research Report , vol.UCB-ITS-RR 99-5
    • Daganzo, C.F.1
  • 18
    • 0021835204 scopus 로고
    • Measure-valued solutions to conservation laws
    • R. J. DIPERNA, Measure-valued solutions to conservation laws, Arch. Ration. Mech. Anal., 88 (1985), pp. 223-270.
    • (1985) Arch. Ration. Mech. Anal. , vol.88 , pp. 223-270
    • Diperna, R.J.1
  • 19
    • 84974746742 scopus 로고
    • Correctors for the homogenization of conservation laws with oscillatory forcing terms
    • E. WEINAN AND D. SERRE, Correctors for the homogenization of conservation laws with oscillatory forcing terms, Asymptot. Anal., 5 (1992), pp. 311-316.
    • (1992) Asymptot. Anal. , vol.5 , pp. 311-316
    • Weinan, E.1    Serre, D.2
  • 21
    • 0035589103 scopus 로고    scopus 로고
    • Effective Hamiltonians and averaging for Hamiltonian dynamics I
    • L. C. EVANS AND D. GOMES, Effective Hamiltonians and averaging for Hamiltonian dynamics I, Arch. Ration. Mech. Anal., 157 (2001), pp. 1-33.
    • (2001) Arch. Ration. Mech. Anal. , vol.157 , pp. 1-33
    • Evans, L.C.1    Gomes, D.2
  • 22
    • 0000876232 scopus 로고
    • Nonlinear follow-the-leader models of traffic flow
    • D. C. GAZIS, R. HERMAN, AND R. W. ROTHERY, Nonlinear follow-the-leader models of traffic flow, Oper. Res., 9 (1961), pp. 545-567.
    • (1961) Oper. Res. , vol.9 , pp. 545-567
    • Gazis, D.C.1    Herman, R.2    Rothery, R.W.3
  • 23
    • 0036306864 scopus 로고    scopus 로고
    • Extensions and amplifications of a traffic model of Aw and Rascle
    • J. M. GREENBERG, Extensions and amplifications of a traffic model of Aw and Rascle, SIAM J. Appl. Math., 62 (2001), pp. 729-745.
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 729-745
    • Greenberg, J.M.1
  • 25
    • 0033196472 scopus 로고    scopus 로고
    • Stability of conservation laws with discontinuous coefficients
    • R. A. KLAUSEN AND N. H. RISEBRO, Stability of conservation laws with discontinuous coefficients, J. Differential Equations, 157 (1999), pp. 41-60.
    • (1999) J. Differential Equations , vol.157 , pp. 41-60
    • Klausen, R.A.1    Risebro, N.H.2
  • 26
    • 0000055941 scopus 로고
    • Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior
    • C. KLINGENBERG AND N. RISEBRO, Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior, Comm. Partial Differential Equations, 20 (1995), pp. 1959-1990.
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 1959-1990
    • Klingenberg, C.1    Risebro, N.2
  • 27
    • 84956238079 scopus 로고
    • First order quasilinear equations with several independent variables
    • S. N. KRUZKOV, First order quasilinear equations with several independent variables, Mat. USSR Sb., 10 (1970), pp. 217-243.
    • (1970) Mat. USSR Sb. , vol.10 , pp. 217-243
    • Kruzkov, S.N.1
  • 30
  • 31
    • 0001764754 scopus 로고
    • -1, q est compacte pour tout q < 2
    • -1, q est compacte pour tout q < 2, J. Math. Pures Appl. (9), 60 (1981), pp. 309-322.
    • (1981) J. Math. Pures Appl. (9) , vol.60 , pp. 309-322
    • Murat, F.1
  • 32
    • 0033475055 scopus 로고    scopus 로고
    • Remarks on the long time behaviour of the solutions of Hamilton-Jacobi equations
    • G. NAMAH AND J. M. ROQUEJOFFRE, Remarks on the long time behaviour of the solutions of Hamilton-Jacobi equations, Comm. Partial Differential Equations, 24 (1999), pp. 883-893.
    • (1999) Comm. Partial Differential Equations , vol.24 , pp. 883-893
    • Namah, G.1    Roquejoffre, J.M.2
  • 34
    • 0343476100 scopus 로고
    • On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws
    • M. RASCLE, On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéaire, 8 (1991), pp. 333-350.
    • (1991) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.8 , pp. 333-350
    • Rascle, M.1
  • 37
    • 0037295910 scopus 로고    scopus 로고
    • Analysis and approximation of a scalar consevation law with a flux function with discontinuous coefficients
    • N. SEGUIN AND J. VOVELLE, Analysis and approximation of a scalar consevation law with a flux function with discontinuous coefficients, Math. Models Methods Appl. Sci., 13 (2003), pp. 221-257.
    • (2003) Math. Models Methods Appl. Sci. , vol.13 , pp. 221-257
    • Seguin, N.1    Vovelle, J.2
  • 40
    • 0001137470 scopus 로고
    • An existence result for scalar conservation laws using measure valued solutions
    • A. SZEPESSY, An existence result for scalar conservation laws using measure valued solutions, Comm. Partial Differential Equations, 14 (1989), pp. 1329-1350.
    • (1989) Comm. Partial Differential Equations , vol.14 , pp. 1329-1350
    • Szepessy, A.1
  • 41
    • 0000440966 scopus 로고
    • Compensated compactness and applications to partial differential equations
    • Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Volume IV, Pitman, Boston
    • L. TARTAR, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Volume IV, Res. Notes in Math. 39, Pitman, Boston, 1979, pp. 136-212.
    • (1979) Res. Notes in Math. , vol.39 , pp. 136-212
    • Tartar, L.1
  • 42
    • 0000967284 scopus 로고
    • Systems of conservation laws with coinciding shock and rarefaction curves
    • J. BLAKE TEMPLE, Systems of conservation laws with coinciding shock and rarefaction curves, Contemp. Math., 17 (1983), pp. 143-151.
    • (1983) Contemp. Math. , vol.17 , pp. 143-151
    • Temple, J.B.1
  • 43
    • 0037529880 scopus 로고    scopus 로고
    • Well-posedness theory of an inhomogeneous traffic flow model
    • L. TONG, Well-posedness theory of an inhomogeneous traffic flow model, Discrete Contin. Dyn. Syst. Ser. B, 2 (2002), pp. 401-414.
    • (2002) Discrete Contin. Dyn. Syst. Ser. B , vol.2 , pp. 401-414
    • Tong, L.1
  • 44
    • 0034449655 scopus 로고    scopus 로고
    • Convergence of a difference scheme for conservation laws with a discontinuous flux
    • J. D. TOWERS, Convergence of a difference scheme for conservation laws with a discontinuous flux, SIAM J. Numer. Anal., 38 (2000), pp. 681-698.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 681-698
    • Towers, J.D.1
  • 45
    • 3142659820 scopus 로고    scopus 로고
    • private communication
    • A. VASSEUR, private communication.
    • Vasseur, A.1
  • 46
    • 0001312217 scopus 로고
    • Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions
    • D.H. WAGNER, Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions, J. Differential Equations, 68 (1987), pp. 118-136.
    • (1987) J. Differential Equations , vol.68 , pp. 118-136
    • Wagner, D.H.1
  • 47
    • 0003342626 scopus 로고
    • Linear and nonlinear waves
    • Wiley-Interscience, New York
    • G. B. WHITHAM, Linear and Nonlinear Waves, Pure and Applied Mathematics, Wiley-Interscience, New York, 1974.
    • (1974) Pure and Applied Mathematics
    • Whitham, G.B.1
  • 48
    • 0036832844 scopus 로고    scopus 로고
    • A multi-class traffic flow model - An extension of LWR model with heterogeneous drivers
    • G. C. K. WONG AND S. C. WONG, A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers, Transportation Research Part A, 36 (2002), pp. 827-841.
    • (2002) Transportation Research Part A , vol.36 , pp. 827-841
    • Wong, G.C.K.1    Wong, S.C.2
  • 49
    • 0036497648 scopus 로고    scopus 로고
    • A non-equilibrium traffic model devoid of gas-like behavior
    • H. M. ZHANG, A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research Part B, 36 (2002), pp. 275-90.
    • (2002) Transportation Research Part B , vol.36 , pp. 275-290
    • Zhang, H.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.