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Volumn 42, Issue 4, 2010, Pages 1761-1783

Vanishing viscosity for traffic on networks

Author keywords

Compensated compactness; Conservation laws; Networks; Traffic model; Vanishing viscosity

Indexed keywords

COMPENSATED COMPACTNESS; CONSERVATION LAWS; NETWORKS; TRAFFIC MODEL; VANISHING VISCOSITY;

EID: 77956082702     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/090771417     Document Type: Article
Times cited : (40)

References (26)
  • 4
    • 23744450066 scopus 로고    scopus 로고
    • Vanishing viscosity solutions of nonlinear hyperbolic systems
    • S. Bianchini and A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems, Ann. of Math. (2), 161 (2005), pp. 223-342.
    • (2005) Ann. of Math. (2) , vol.161 , pp. 223-342
    • Bianchini, S.1    Bressan, A.2
  • 5
    • 0002063363 scopus 로고    scopus 로고
    • Vanishing viscosity limit for initial-boundary value problems for conservation laws. Nonlinear partial differential equations
    • G.-Q. Chen and H. Frid, Vanishing viscosity limit for initial-boundary value problems for conservation laws. Nonlinear partial differential equations, Contemp. Math., 238 (1999), pp. 35-51.
    • (1999) Contemp. Math. , vol.238 , pp. 35-51
    • Chen, G.-Q.1    Frid, H.2
  • 8
  • 9
    • 52649143184 scopus 로고    scopus 로고
    • On the Cauchy problem for the p-system at a junction
    • R. M. Colombo and M. Garavello, On the Cauchy problem for the p-system at a junction, SIAM J. Math. Anal., 39 (2008), pp. 1456-1471.
    • (2008) SIAM J. Math. Anal. , vol.39 , pp. 1456-1471
    • Colombo, R.M.1    Garavello, M.2
  • 10
    • 34548247698 scopus 로고    scopus 로고
    • Wave Propagation, observation, and control in 1-d flexible multistructures
    • Springer-Verlag, Berlin
    • R. Dáger and E. Zuazua, Wave Propagation, Observation, and Control in 1-d Flexible Multistructures, Math. Appl. 50, Springer-Verlag, Berlin, 2006.
    • (2006) Math. Appl. , vol.50
    • Dáger, R.1    Zuazua, E.2
  • 11
    • 31744447286 scopus 로고    scopus 로고
    • Traffic flow on a road network using the Aw-Rascle model
    • M. Garavello and B. Piccoli, Traffic flow on a road network using the Aw-Rascle model, Comm. Partial Differential Equations, 31 (2006), pp. 243-275.
    • (2006) Comm. Partial Differential Equations , vol.31 , pp. 243-275
    • Garavello, M.1    Piccoli, B.2
  • 12
    • 52649154469 scopus 로고    scopus 로고
    • Traffic flow on networks: Conservation laws models
    • American Institute of Mathematical Sciences, Springfield, MO
    • M. Garavello and B. Piccoli, Traffic Flow on Networks: Conservation Laws Models, AIMS Ser. Appl. Math. 1, American Institute of Mathematical Sciences, Springfield, MO, 2006.
    • (2006) AIMS Ser. Appl. Math. , vol.1
    • Garavello, M.1    Piccoli, B.2
  • 13
    • 77956077408 scopus 로고    scopus 로고
    • Quaderno n. 9/2009 del Dipartimento di Matematica e Applicazioni, University of Milano Bicocca, Milan, Italy; available online from
    • M. Garavello and B. Piccoli, Entropy Type Conditions for Riemann Solvers at Nodes, Quaderno n. 9/2009 del Dipartimento di Matematica e Applicazioni, University of Milano Bicocca, Milan, Italy; available online from http://arxiv.org/PS cache/arxiv/pdf/0905/ 0905.4408v1.pdf.
    • Entropy Type Conditions for Riemann Solvers at Nodes
    • Garavello, M.1    Piccoli, B.2
  • 14
    • 54049085644 scopus 로고    scopus 로고
    • Vanishing viscosity boundary layers for nonlinear hyperbolic systems
    • Nonlinear Theory of Generalized Functions (Vienna, 1997) , Chapman & Hall/CRC, Boca Raton, FL
    • O. Guès, Vanishing viscosity boundary layers for nonlinear hyperbolic systems, in Nonlinear Theory of Generalized Functions (Vienna, 1997), Chapman Hall/CRC Res. Notes Math. 401, Chapman & Hall/CRC, Boca Raton, FL, 1999, pp. 75-84.
    • (1999) Chapman Hall/CRC Res. Notes Math. , vol.401 , pp. 75-84
    • Guès, O.1
  • 15
    • 0041920783 scopus 로고
    • A mathematical model of traffic flow on a network of unidirectional roads
    • H. Holden and N. H. Risebro, A mathematical model of traffic flow on a network of unidirectional roads, SIAM J. Math. Anal., 26 (1995), pp. 999-1017.
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 999-1017
    • Holden, H.1    Risebro, N.H.2
  • 16
    • 85067915698 scopus 로고    scopus 로고
    • Front tracking for hyperbolic conservation laws
    • Springer-Verlag, New York
    • H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Conservation Laws, Appl. Math. Sci. 152, Springer-Verlag, New York, 2002.
    • (2002) Appl. Math. Sci. , vol.152
    • Holden, H.1    Risebro, N.H.2
  • 17
    • 0000989705 scopus 로고
    • Off diagonal short time asymptotics for fundamental solutions of diffusion equations
    • Y. Kannai, Off diagonal short time asymptotics for fundamental solutions of diffusion equations, Comm. Partial Differ. Equations, 2 (1977), pp. 781-830.
    • (1977) Comm. Partial Differ. Equations , vol.2 , pp. 781-830
    • Kannai, Y.1
  • 18
    • 0000220623 scopus 로고
    • First order quasilinear equations with several independent variables
    • S. N. Kružkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.), 81 (1970), pp. 228-255.
    • (1970) Mat. Sb. (N.S.) , vol.81 , pp. 228-255
    • Kružkov, S.N.1
  • 19
    • 0000090588 scopus 로고
    • On kinematic waves. II. A theory of traffic flow on long crowded roads
    • 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), pp. 317-345.
    • (1955) Proc. Roy. Soc. London. Ser. A. , vol.229 , pp. 317-345
    • Lighthill, M.J.1    Whitham, G.B.2
  • 20
    • 33947155454 scopus 로고    scopus 로고
    • Gaussian estimates for a heat equation on a network
    • D. Mugnolo, Gaussian estimates for a heat equation on a network, Netw. Heterog. Media, 2 (2007), pp. 55-79.
    • (2007) Netw. Heterog. Media , vol.2 , pp. 55-79
    • Mugnolo, D.1
  • 21
    • 0001764754 scopus 로고
    • q est compacte pour tout q < 2
    • 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
  • 22
    • 0002842180 scopus 로고
    • Shock waves on the highway
    • P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), pp. 42-51.
    • (1956) Operations Res. , vol.4 , pp. 42-51
    • Richards, P.I.1
  • 23
    • 12344331631 scopus 로고    scopus 로고
    • Characteristic boundary layers in real vanishing viscosity limits
    • F. Rousset, Characteristic boundary layers in real vanishing viscosity limits, J. Differential Equations, 210 (2005), pp. 25-64.
    • (2005) J. Differential Equations , vol.210 , pp. 25-64
    • Rousset, F.1
  • 24
    • 0036014240 scopus 로고    scopus 로고
    • The residual boundary conditions coming from the real vanishing viscosity method
    • F. Rousset, The residual boundary conditions coming from the real vanishing viscosity method, Discrete Contin. Dyn. Syst., 8 (2002), pp. 605-625.
    • (2002) Discrete Contin. Dyn. Syst. , vol.8 , pp. 605-625
    • Rousset, F.1
  • 25
    • 0035536781 scopus 로고    scopus 로고
    • Boundary layer stability in real vanishing viscosity limit
    • D. Serre and K. Zumbrun, Boundary layer stability in real vanishing viscosity limit, Comm. Math. Phys., 221 (2001), pp. 267-292.
    • (2001) Comm. Math. Phys. , vol.221 , pp. 267-292
    • Serre, D.1    Zumbrun, K.2
  • 26
    • 0000440966 scopus 로고
    • Compensated compactness and applications to partial differential equations
    • Pitman, Boston
    • L. Tartar, Compensated Compactness and Applications to Partial Differential Equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol.IV, Pitman, Boston, 1979, pp. 136-212.
    • (1979) Nonlinear Analysis and Mechanics: Heriot-Watt Symposium , vol.4 , pp. 136-212
    • Tartar, L.1


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