메뉴 건너뛰기




Volumn 16, Issue 16, 2006, Pages 733-748

Weak formulation of boundary conditions for scalar conservation laws: An application to highway traffic modelling

Author keywords

Boundary control; Highway traffic modelling; LWR PDE; Weak solution of scalar conservation laws

Indexed keywords

BOUNDARY CONDITIONS; FUNCTION EVALUATION; MATHEMATICAL MODELS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33750582904     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1099     Document Type: Article
Times cited : (64)

References (49)
  • 1
    • 23944525905 scopus 로고    scopus 로고
    • Localized switching rampmetering controller with queue length regulator for congested freeways
    • Portland, June
    • Sun X, Horowitz R. Localized switching rampmetering controller with queue length regulator for congested freeways. Proceedings of the American Control Conference, Portland, June 2005; 2141-2146.
    • (2005) Proceedings of the American Control Conference , pp. 2141-2146
    • Sun, X.1    Horowitz, R.2
  • 2
    • 0000090588 scopus 로고
    • On kinematic waves. II. A theory of traffic flow on long crowded roads
    • Lighthill MJ, Whitham GB. On kinematic waves. II. A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London 1956; 229(1178):317-345.
    • (1956) Proceedings of the Royal Society of London , vol.229 , Issue.1178 , pp. 317-345
    • Lighthill, M.J.1    Whitham, G.B.2
  • 3
    • 0002842180 scopus 로고
    • Shock waves on the highway
    • Richards PI. Shock waves on the highway. Operations Research 1956; 4(1):42-51.
    • (1956) Operations Research , vol.4 , Issue.1 , pp. 42-51
    • Richards, P.I.1
  • 5
    • 0001054808 scopus 로고    scopus 로고
    • On global stabilization of Burgers' equation by boundary control
    • Krstić M. On global stabilization of Burgers' equation by boundary control. Systems and Control Letters 1999; 37:123-142.
    • (1999) Systems and Control Letters , vol.37 , pp. 123-142
    • Krstić, M.1
  • 6
    • 0002281210 scopus 로고
    • On discontinuous solutions of nonlinear differential equations
    • Oleinik OA. On discontinuous solutions of nonlinear differential equations. Uspekhi Matematichiskish Nauk 1957; 12:3-73.
    • (1957) Uspekhi Matematichiskish Nauk , vol.12 , pp. 3-73
    • Oleinik, O.A.1
  • 7
    • 0002717472 scopus 로고
    • English translation
    • (English translation: American Mathematical Society 1963; 26(2):95-172.)
    • (1963) American Mathematical Society , vol.26 , Issue.2 , pp. 95-172
  • 8
    • 0025417832 scopus 로고
    • What does the entropy condition mean in traffic flow theory?
    • Ansorge R. What does the entropy condition mean in traffic flow theory? Transportation Research 1990; 24B(2): 133-143.
    • (1990) Transportation Research , vol.24 B , Issue.2 , pp. 133-143
    • Ansorge, R.1
  • 9
    • 0028803659 scopus 로고
    • The cell transmission model, part II: Network traffic
    • Daganzo C. The cell transmission model, part II: network traffic. Transportation Research 1995; 29B(2):79-93.
    • (1995) Transportation Research , vol.29 B , Issue.2 , pp. 79-93
    • Daganzo, C.1
  • 11
    • 33750584611 scopus 로고    scopus 로고
    • Berkeley Highway Laboratory
    • Berkeley Highway Laboratory. http://bhl.its.berkeley.edu:9006/bhl/index. html
  • 12
    • 0000935266 scopus 로고
    • A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics
    • Godunov SK. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Mathematics of the Sbornik 1959; 47:271-306.
    • (1959) Mathematics of the Sbornik , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 13
    • 84954695021 scopus 로고
    • Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence
    • Jameson A. Analysis and design of numerical schemes for gas dynamics 1: artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. International Journal of Computational Fluid Dynamics 1995; 4:171-218.
    • (1995) International Journal of Computational Fluid Dynamics , vol.4 , pp. 171-218
    • Jameson, A.1
  • 14
    • 84864361143 scopus 로고
    • Analysis and design of numerical schemes for gas dynamics 2: Artificial diffusion and discrete shock structure
    • Jameson A. Analysis and design of numerical schemes for gas dynamics 2: artificial diffusion and discrete shock structure. International Journal of Computational Fluid Dynamics 1995; 4:1-38.
    • (1995) International Journal of Computational Fluid Dynamics , vol.4 , pp. 1-38
    • Jameson, A.1
  • 15
    • 0028481056 scopus 로고
    • The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory
    • Daganzo C. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research 1994; 28B(4):269-287.
    • (1994) Transportation Research , vol.28 B , Issue.4 , pp. 269-287
    • Daganzo, C.1
  • 21
  • 23
    • 0002810672 scopus 로고
    • An analysis of traffic flow
    • Greenberg H. An analysis of traffic flow. Operation Research 1959; 7(1):79-85.
    • (1959) Operation Research , vol.7 , Issue.1 , pp. 79-85
    • Greenberg, H.1
  • 24
    • 84988147318 scopus 로고
    • Explicit formula for scalar non-linear conservation laws with boundary condition
    • Le Floch P. Explicit formula for scalar non-linear conservation laws with boundary condition. Mathematical Methods in the Applied Sciences 1988; 10:265-287.
    • (1988) Mathematical Methods in the Applied Sciences , vol.10 , pp. 265-287
    • Le Floch, P.1
  • 25
    • 84956238079 scopus 로고
    • First order quasilinear equations in several independent variables
    • Kruz̀kov SN. First order quasilinear equations in several independent variables. Mathematics of The USSR Sbornik 1970; 10:217-243.
    • (1970) Mathematics of the USSR Sbornik , vol.10 , pp. 217-243
    • Kruz̀kov, S.N.1
  • 28
    • 0000869974 scopus 로고
    • Existence of solutions to singular conservation laws
    • Schonbek ME. Existence of solutions to singular conservation laws. Journal of Mathematical Analysis 1984; 15(6):1125-1139.
    • (1984) Journal of Mathematical Analysis , vol.15 , Issue.6 , pp. 1125-1139
    • Schonbek, M.E.1
  • 31
    • 0031672504 scopus 로고    scopus 로고
    • On the attainable set for scalar nonlinear conservations laws with boundary control
    • Ancona F, Marson A. On the attainable set for scalar nonlinear conservations laws with boundary control. SIAM Journal on Control and Optimization 1998; 36(1):290-312.
    • (1998) SIAM Journal on Control and Optimization , vol.36 , Issue.1 , pp. 290-312
    • Ancona, F.1    Marson, A.2
  • 32
    • 0033101711 scopus 로고    scopus 로고
    • Scalar non-linear conservations laws with integrable boundary data
    • Ancona F, Marson A. Scalar non-linear conservations laws with integrable boundary data. Nonlinear Analysis 1999; 35:687-710.
    • (1999) Nonlinear Analysis , vol.35 , pp. 687-710
    • Ancona, F.1    Marson, A.2
  • 33
    • 0000617788 scopus 로고
    • Generalized characteristics and the structure of solutions of hyperbolic conservation laws
    • Dafermos C. Generalized characteristics and the structure of solutions of hyperbolic conservation laws. Indiana Mathematics Journal 1977; 26:1097-1119.
    • (1977) Indiana Mathematics Journal , vol.26 , pp. 1097-1119
    • Dafermos, C.1
  • 36
    • 0031075915 scopus 로고    scopus 로고
    • Comparison properties for scalar conservation laws with boundary conditions
    • Terracina A. Comparison properties for scalar conservation laws with boundary conditions. Nonlinear Analysis - Theory, Methods and Applications 1997; 28:633-653.
    • (1997) Nonlinear Analysis - Theory, Methods and Applications , vol.28 , pp. 633-653
    • Terracina, A.1
  • 38
    • 0001940777 scopus 로고    scopus 로고
    • Viscosity solutions: A primer
    • Lecture Notes in Mathematics Springer: Berlin
    • Crandall MG. Viscosity solutions: a primer. Viscosity Solutions and Applications, Lecture Notes in Mathematics, vol. 1660. Springer: Berlin, 1997; 1-43.
    • (1997) Viscosity Solutions and Applications , vol.1660 , pp. 1-43
    • Crandall, M.G.1
  • 40
    • 0034388593 scopus 로고    scopus 로고
    • Nonlinear control of incompressible fluid flow: Application to Burgers' equation and 2d channel flow
    • Baker J, Armaou A, Christofides PD. Nonlinear control of incompressible fluid flow: application to Burgers' equation and 2d channel flow. Journal of Mathematical Analysis and Applications 2000; 252:230-255.
    • (2000) Journal of Mathematical Analysis and Applications , vol.252 , pp. 230-255
    • Baker, J.1    Armaou, A.2    Christofides, P.D.3
  • 43
    • 10644232760 scopus 로고    scopus 로고
    • International Series in Operations Research and Management Science. Kluwer Academic: Boston
    • Gazis DC. Traffic Theory. International Series in Operations Research and Management Science. Kluwer Academic: Boston, 2002.
    • (2002) Traffic Theory
    • Gazis, D.C.1
  • 44
    • 84973998581 scopus 로고
    • Explicit formula for the solution of convex conservation laws with boundary condition
    • Joseph K.T, Veerappa Gowda GD. Explicit formula for the solution of convex conservation laws with boundary condition. Duke Mathematical Journal 1991; 62(2):401-416.
    • (1991) Duke Mathematical Journal , vol.62 , Issue.2 , pp. 401-416
    • Joseph, K.T.1    Veerappa Gowda, G.D.2
  • 45
    • 0035450991 scopus 로고    scopus 로고
    • Adaptive regulator design of a viscous Burgers' system by boundary control
    • Kobayashi T. Adaptive regulator design of a viscous Burgers' system by boundary control. IM A Journal of Mathematical Control and Information 2001; 18(3):427-437.
    • (2001) IM A Journal of Mathematical Control and Information , vol.18 , Issue.3 , pp. 427-437
    • Kobayashi, T.1
  • 46
    • 0000789836 scopus 로고
    • On the convergence of the Godunov's scheme for first order quasi linear equations
    • Le Roux AY. On the convergence of the Godunov's scheme for first order quasi linear equations. Proceedings of the Japan Academics 1976; 52:488-491.
    • (1976) Proceedings of the Japan Academics , vol.52 , pp. 488-491
    • Le Roux, A.Y.1
  • 49
    • 5044248077 scopus 로고    scopus 로고
    • Low dimensional modelling and Dirichlet boundary controller design for Burgers' equation
    • Önder M, Özbay E. Low dimensional modelling and Dirichlet boundary controller design for Burgers' equation. International Journal of Control 2004; 77(10):895-906.
    • (2004) International Journal of Control , vol.77 , Issue.10 , pp. 895-906
    • Önder, M.1    Özbay, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.