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Volumn 372, Issue 1, 2010, Pages 77-85

On the Cauchy problem for macroscopic model of pedestrian flows

Author keywords

Crowd dynamics; First order hyperbolic system; Singular perturbation; Zero relaxation limit

Indexed keywords


EID: 77955269379     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2010.06.044     Document Type: Article
Times cited : (14)

References (28)
  • 1
    • 0033691480 scopus 로고    scopus 로고
    • Resurrection of "second order" models of traffic flow
    • Aw A., Rascle M. Resurrection of "second order" models of traffic flow. SIAM J. Appl. Math. 2000, 60(3):916-938.
    • (2000) SIAM J. Appl. Math. , vol.60 , Issue.3 , pp. 916-938
    • Aw, A.1    Rascle, M.2
  • 2
    • 48049120920 scopus 로고    scopus 로고
    • On the modelling crowd dynamics from scaling to hyperbolic macroscopic models
    • Bellomo N., Dogbé C. On the modelling crowd dynamics from scaling to hyperbolic macroscopic models. Math. Models Methods Appl. Sci. 2008, 18:1317-1345.
    • (2008) Math. Models Methods Appl. Sci. , vol.18 , pp. 1317-1345
    • Bellomo, N.1    Dogbé, C.2
  • 3
    • 77955272220 scopus 로고    scopus 로고
    • On the modelling of traffic and crowds. A survey of models, speculations, and perspectives, SIAM Rev., in press
    • N. Bellomo, C. Dogbé, On the modelling of traffic and crowds. A survey of models, speculations, and perspectives, SIAM Rev., in press.
    • Bellomo, N.1    Dogbé, C.2
  • 4
    • 84990689276 scopus 로고
    • Hyperbolic conservation laws with stiff relaxation terms and entropy
    • Chen G.-Q., Levermore C.D., Liu T.-P. Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. 1994, 47:787-830.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 787-830
    • Chen, G.-Q.1    Levermore, C.D.2    Liu, T.-P.3
  • 5
    • 49449106664 scopus 로고    scopus 로고
    • First order macroscopic modelling of human crowds
    • Coscia V., Canavesio C. First order macroscopic modelling of human crowds. Math. Models Methods Appl. Sci. 2008, 18:1217-1247.
    • (2008) Math. Models Methods Appl. Sci. , vol.18 , pp. 1217-1247
    • Coscia, V.1    Canavesio, C.2
  • 8
    • 0033119901 scopus 로고    scopus 로고
    • Nonlinear hydrodynamic models of traffic flow modelling and mathematical problems
    • De Angelis E. Nonlinear hydrodynamic models of traffic flow modelling and mathematical problems. Math. Comput. Modelling 1999, 29:83-95.
    • (1999) Math. Comput. Modelling , vol.29 , pp. 83-95
    • De Angelis, E.1
  • 9
    • 84982412190 scopus 로고
    • A mathematical model for the behavior of pedestrians
    • Helbing D. A mathematical model for the behavior of pedestrians. Behavioral Sci. 1991, 36:298-310.
    • (1991) Behavioral Sci. , vol.36 , pp. 298-310
    • Helbing, D.1
  • 10
    • 35949007691 scopus 로고
    • Social force model for pedestrian dynamics
    • Helbing D., Molnár P. Social force model for pedestrian dynamics. Phys. Rev. E 1995, 51:4282-4286.
    • (1995) Phys. Rev. E , vol.51 , pp. 4282-4286
    • Helbing, D.1    Molnár, P.2
  • 11
    • 0034727079 scopus 로고    scopus 로고
    • Simulating dynamical feature of escape panic
    • Helbing D., Farkas I., Vicsek T. Simulating dynamical feature of escape panic. Nature 2000, 407:487-490.
    • (2000) Nature , vol.407 , pp. 487-490
    • Helbing, D.1    Farkas, I.2    Vicsek, T.3
  • 12
    • 0000736872 scopus 로고    scopus 로고
    • A fluid-dynamic model for the movement of pedestrians
    • Helbing D. A fluid-dynamic model for the movement of pedestrians. Complex Systems 2002, 6:391-415.
    • (2002) Complex Systems , vol.6 , pp. 391-415
    • Helbing, D.1
  • 13
    • 35248856713 scopus 로고
    • The statistics of crowd fluids
    • Henderson L.F. The statistics of crowd fluids. Nature 1971, 229:381-383.
    • (1971) Nature , vol.229 , pp. 381-383
    • Henderson, L.F.1
  • 14
    • 0016336636 scopus 로고
    • On the fluid mechanic of human crowd motion
    • Henderson L.F. On the fluid mechanic of human crowd motion. Transp. Res. 1975, 8:509-515.
    • (1975) Transp. Res. , vol.8 , pp. 509-515
    • Henderson, L.F.1
  • 15
    • 0015498624 scopus 로고
    • Sexual differences in human crowds motion
    • Henderson L.F., Lyons D.J. Sexual differences in human crowds motion. Nature 1972, 240:353-355.
    • (1972) Nature , vol.240 , pp. 353-355
    • Henderson, L.F.1    Lyons, D.J.2
  • 16
    • 0016026954 scopus 로고
    • Response of pedestrians to traffic challenge
    • Henderson L.F., Jenkins D.M. Response of pedestrians to traffic challenge. Transp. Res. 1973, 8:71.
    • (1973) Transp. Res. , vol.8 , pp. 71
    • Henderson, L.F.1    Jenkins, D.M.2
  • 17
    • 0036643318 scopus 로고    scopus 로고
    • A continuum theory for the flow of pedestrians
    • Hughes R.L. A continuum theory for the flow of pedestrians. Transp. Res. B 2002, 36:507-536.
    • (2002) Transp. Res. B , vol.36 , pp. 507-536
    • Hughes, R.L.1
  • 18
    • 0346245136 scopus 로고    scopus 로고
    • The flow of human crowds
    • Hughes R.L. The flow of human crowds. Annu. Rev. Fluid Mech. 2003, 35:169-183.
    • (2003) Annu. Rev. Fluid Mech. , vol.35 , pp. 169-183
    • Hughes, R.L.1
  • 19
    • 84990701264 scopus 로고
    • The relaxation schemes for systems of conservation laws in arbitrary space dimensions
    • Jin S., Xin Z. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 1995, 48:235-276.
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 235-276
    • Jin, S.1    Xin, Z.2
  • 20
    • 0035581884 scopus 로고    scopus 로고
    • Convergence of a relaxation scheme for hyperbolic systems of conservation laws
    • Lattanzio C., Serre D. Convergence of a relaxation scheme for hyperbolic systems of conservation laws. Numer. Math. 2001, 88:121-134.
    • (2001) Numer. Math. , vol.88 , pp. 121-134
    • Lattanzio, C.1    Serre, D.2
  • 21
    • 0003202932 scopus 로고
    • Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
    • Springer, New York
    • Majda A. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Appl. Math. Sci. 1984, vol. 53. Springer, New York.
    • (1984) Appl. Math. Sci. , vol.53
    • Majda, A.1
  • 22
    • 68149136534 scopus 로고    scopus 로고
    • Pedestrian flows in bounded domains with obstacles
    • Piccoli B., Tosin A. Pedestrian flows in bounded domains with obstacles. Contin. Mech. Thermodyn. 2009, 21:85-107.
    • (2009) Contin. Mech. Thermodyn. , vol.21 , pp. 85-107
    • Piccoli, B.1    Tosin, A.2
  • 25
    • 0347985905 scopus 로고
    • Topics in singular perturbations
    • O'Malley R.E. Topics in singular perturbations. Adv. Math. 1968, 2:365-470.
    • (1968) Adv. Math. , vol.2 , pp. 365-470
    • O'Malley, R.E.1
  • 26
    • 33750958713 scopus 로고    scopus 로고
    • Crowd dynamics on a moving platform: Mathematical modelling and application to lively footbridges
    • Venuti F., Bruno L., Bellomo N. Crowd dynamics on a moving platform: Mathematical modelling and application to lively footbridges. Math. Comput. Modelling 2007, 45:252-269.
    • (2007) Math. Comput. Modelling , vol.45 , pp. 252-269
    • Venuti, F.1    Bruno, L.2    Bellomo, N.3
  • 28
    • 0033542203 scopus 로고    scopus 로고
    • Singular perturbations of first-order hyperbolic systems with stiff source terms
    • Yong W.-A. Singular perturbations of first-order hyperbolic systems with stiff source terms. J. Differential Equations 1999, 155(1):89-132.
    • (1999) J. Differential Equations , vol.155 , Issue.1 , pp. 89-132
    • Yong, W.-A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.