Nonlocal Crowd Dynamics Models for Several Populations

Acta Mathematica Scientia

Volumn 32, Issue 1, 2012, Pages 177-196

  Colombo, Rinaldo M ^a   Lécureux Mercier, Magali ^b  

^a UNIVERSITY OF BRESCIA   (Italy)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

35L65; Hyperbolic conservation laws; Nonlocal flow; Pedestrian traffic

Indexed keywords

EID: 84856107559     PISSN: 02529602     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0252-9602(12)60011-3     Document Type: Article

References (15)

1. Appert-Rolland C, Degond P, Motsch S Two-way multi-lane traffic model for pedestrians in corridors. Networks and Heterogeneous Media 2011, 6(3):351-381.
2. Bellomo N, Dogbé C On the modelling of traffic and crowds - a survey of models, speculations, and perspectives. SIAM Review 2011, 53(3):409-463.
3. Bressan A, Guerra G Shift-differentiability of the flow generated by a conservation law. Discrete Contin Dynam Systems 1997, 3(1):35-58.
4. Colombo R M, Facchi G, Maternini G, Rosini M D. On the continuum modeling of crowds//Proceedings of Hyp2008 - the twelfth International Conference on Hyperbolic Problems held in the University of Maryland, College Park, June 2008. Hyperbolic Problems: Theory, Numerics and Applications. Acer Math Soc, 2009: 517-526.
5. Colombo RM, Garavello M, Lécureux-Mercier M. A class of non-local models for pedestrian traffic. Preprint, 2010.
6. Colombo RM, Herty M, Mercier M Control of the continuity equation with a non local flow. ESAIM: Control Optim Calcu Var 2011, 17(2):353-379.
7. Colombo RM, Mercier M, Rosini MD Stability and total variation estimates on general scalar balance laws. Commun Math Sci 2009, 7(1):37-65.
8. Crippa G, Lécureux-Mercier M. Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow. Preprint, 2011.
9. Cristiani E, Piccoli B, Tosin A Multiscale modeling of granular flows with application to crowd dynamics. Multiscale Modeling & Simulation 2011, 9(1):155-182.
10. Daamen W, Hoogendoorn S Experimental research of pedestrian walking behavior. Transportation Research Board annual meeting 2003 2007, 1-16. National Academy Press.
11. Dafermos CM Hyperbolic Conservation Laws in Continuum Physics. Volume 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 2005, Springer-Verlag, Berlin. 2nd ed.
12. Helbing D, Molnár P, Farkas I, Bolay K Self-organizing pedestrian movement. Environment and Planning B: Planning and Design 2001, 28:361-383.
13. KruŠkov SN First order quasilinear equations with several independent variables. Mat Sb (N S) 1970, 81(123):228-255.
14. Lécureux-Mercier M. Improved stability estimates on general scalar balance laws. To appear on J of Hyperbolic Differential Equations, 2011.
15. Levy R, Shearer M The motion of a thin liquid film driven by surfactant and gravity. SIAM J Appl Math 2006, 66(5):1588-1609.