A class of nonlocal models for pedestrian traffic

Mathematical Models and Methods in Applied Sciences

Volumn 22, Issue 4, 2012, Pages

  Colombo, Rinaldo M ^a   Garavello, Mauro ^b   LÉcureux Mercier, Magali ^c  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITY OF EASTERN PIEDMONT   (Italy)

^c UNIVERSITÉ D'ORLÉANS   (France)

Author keywords

Crowd dynamics; macroscopic pedestrian model; nonlocal conservation laws

Indexed keywords

BEST PATHS; BOUNDEDNESS; CONSERVATION LAW; CROWD DENSITY; CROWD DYNAMICS; EXIT TIME; FIXED TARGETS; LIPSCHITZ; MACROSCOPIC MODEL; NONLOCAL; NONLOCAL MODELS; NUMERICAL INTEGRATIONS; PEDESTRIAN FLOW; PEDESTRIAN MODELS; PEDESTRIAN TRAFFIC; QUALITATIVE PROPERTIES; SEMI-GROUP;

COMPUTER SIMULATION; MATHEMATICAL MODELS;

PHYSICAL PROPERTIES;

EID: 84857745912     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202511500230     Document Type: Article

References (30)

1. N. Bellomo and C. Dogbé, On the modelling crowd dynamics from scaling to hyperbolic macroscopic models, Math. Models Methods Appl. Sci. 18(SUPPL.) (2008) 1317-1345.
2. N. Bellomo and C. Dogbé, On the modelling of traffic and crowds. A survey of models, speculations, and perspectives, SIAM Rev. 53 (2011) 409-463.
3. A. Bressan, Hyperbolic Systems of Conservation Laws, Oxford Lecture Series in Mathematics and Its Applications, Vol. 20 (Oxford Univ. Press, 2000).
4. A. Bressan and R. M. Colombo, P.D.E. models of pedestrian flow, unpublished, 2007.
5. J. V. Burke, A. S. Lewis and M. L. Overton, A robust gradient sampling algorithm for nonsmooth, nonconvex optimization, SIAM J. Optim. 15 (2005) 751-779. (Pubitemid 41156914)
6. G. Buttazzo, C. Jimenez and E. Oudet, An optimization problem for mass transportation with congested dynamics, SIAM J. Control Optim. 48 (2009) 1961-1976.
7. C. Chalons, Numerical approximation of a macroscopic model of pedestrian flows, SIAM J. Sci. Comput. 29 (electronic) (2007) 539-555. (Pubitemid 351456404)
8. R. M. Colombo, M. Herty and M. Mercier, Control of the continuity equation with a non local flow, ESAIM: COCV 17 (2011) 353-379.
9. R. M. Colombo and M. Mercier, An analytical framework to describe the interactions between individuals and a continuum, J. Nonlinear Sci., to appear.
10. R. M. Colombo, M. Mercier and M. D. Rosini, Stability and total variation estimates on general scalar balance laws, Commun. Math. Sci. 7 (2009) 37-65.
11. R. M. Colombo and M. D. Rosini, Pedestrian flows and non-classical shocks, Math. Methods Appl. Sci. 28 (2005) 1553-1567. (Pubitemid 41203749)
12. R. M. Colombo and M. D. Rosini, Existence of nonclassical solutions in a pedestrian flow model, Nonlinear Anal. Real World Appl. 10 (2009) 2716-2728.
13. V. Coscia and C. Canavesio, First-order macroscopic modelling of human crowd dynamics, Math. Models Methods Appl. Sci. 18(SUPPL.) (2008) 1217-1247.
14. E. Cristiani, B. Piccoli and A. Tosin, Multiscale modeling of granular flows with application to crowd dynamics, Multiscale Model. Simulat. 9 (2011) 155-182.
15. M. Di Francesco, P. A. Markowich, J.-F. Pietschmann and M.-T. Wolfram, On the Hughes' model for pedestrian flow: The one-dimensional case, J. Differential Equations 250 (2011) 1334-1362.
16. C. Dogbé, Modeling crowd dynamics by the mean-field limit approach, Math. Comput. Model. 52 (2010) 1506-1520.
17. C. Dogbé, On the Cauchy problem for macroscopic model of pedestrian flows, J. Math. Anal. Appl. 372 (2010) 77-85.
18. D. Helbing, I. Farkás, P. Molnár and T. Vicsek, Simulation of pedestrian crowds in normal and evacuation situations, in Pedestrian and Evacuation Dynamics, eds. M. Schreckenberg and S. D. Sharma (Springer, 2002), pp. 21-58.
19. D. Helbing and A. Johansson, Quantitative agent-based modeling of human interactions in space and time, in Proc. 4th Conf. of the European Social Simulation Association, ed. F. Amblard (2007), pp. 623-637.
20. D. Helbing and A. Johansson, Pedestrian, crowd and evacuation dynamics, in Encyclopedia of Complexity and Systems Science (2010), pp. 6476-6495.
21. S. Hoogendoorn and P. H. L. Bovy, Simulation of pedestrian flows by optimal control and differential games, Optimal Control Appl. Methods 24 (2003) 153-172.
22. S. Hoogendoorn and P. H. L. Bovy, Pedestrian route-choice and activity scheduling theory and model, Transp. Res. B 38 (2004) 169-190. (Pubitemid 37515111)
23. R. L. Hughes, A continuum theory for the flow of pedestrians, Transp. Res. Part B: Methodological 36 (2002) 507-535. (Pubitemid 34444175)
24. R. L. Hughes, The flow of human crowds, Ann. Rev. Fluid Mech. 35 (2003) 169-182. (Pubitemid 37519344)
25. S. N. Kružkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.) 81 (1970) 228-255.
26. M. Lécureux-Mercier, Improved stability estimates on general scalar balance laws, J. Hyperbolic Differential Equations, to appear.
27. B. Maury, A. Roudneff-Chupin and F. Santambrogio, A macroscopic crowd motion model of the gradient-flow type, Math. Models Methods Appl. Sci. 20 (2010) 1787-1821.
28. B. Maury, A. Roudneff-Chupin, F. Santambrogio and J. Venel, Handling congestion in crowd motion modeling, Netw. Heterog. Media 6 (2011) 485-519.
29. B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn. 21 (2009) 85-107.
30. B. Piccoli and A. Tosin, Time-evolving measures and macroscopic modeling of pedestrian flow, Arch. Rational Mech. Anal. 199 (2011) 707-738.