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Empirical results for pedestrian dynamics and their implications for modeling
Existence and approximation of probability measure solutions to models of collective behaviors
1.  Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy 
References:
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L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," 2^{nd} edition, Birkhäuser Verlag, Basel, 2008. Google Scholar 
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N. Bellomo, "Modeling Complex Living Systems. A Kinetic Theory and Stochastic Game Approach," Birkhäuser, Boston, 2008. Google Scholar 
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J. A. Cañizo, J. A. Carrillo and J. Rosado, A wellposedness theory in measures for some kinetic models of collective motion, Math. Models Methods Appl. Sci., 21 (2011), 515539. doi: 10.1142/S0218202511005131. Google Scholar 
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C. Canuto, F. Fagnani and P. Tilli, A Eulerian approach to the analysis of rendezvous algorithms, in "Proceedings of the 17th IFAC World Congress", (2008), 90399044. Google Scholar 
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E. Cristiani, P. Frasca and B. Piccoli, Effects of anisotropic interactions on the structure of animal groups, J. Math. Biol., 62 (2011), 569588. doi: 10.1007/s0028501003477. Google Scholar 
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E. Cristiani, B. Piccoli and A. Tosin, Modeling selforganization in pedestrian and animal groups from macroscopic and microscopic viewpoints, in "Mathematical Modeling of Collective Behavior in SocioEconomic and Life Sciences" (eds. G. Naldi, L. Pareschi and G. Toscani), Birkhäuser, Boston, (2010), 337364. Google Scholar 
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R. J. LeVeque, "Numerical Methods for Conservation Laws," 2^{nd} edition, Birkhäuser Verlag, Basel, 1992. Google Scholar 
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B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn., 21 (2009), 85107. doi: 10.1007/s001610090100x. Google Scholar 
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B. Piccoli and A. Tosin, Timeevolving measures and macroscopic modeling of pedestrian flow, Arch. Ration. Mech. Anal., 199 (2011), 707738. doi: 10.1007/s002050100366y. Google Scholar 
show all references
References:
[1] 
L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," 2^{nd} edition, Birkhäuser Verlag, Basel, 2008. Google Scholar 
[2] 
N. Bellomo, "Modeling Complex Living Systems. A Kinetic Theory and Stochastic Game Approach," Birkhäuser, Boston, 2008. Google Scholar 
[3] 
J. A. Cañizo, J. A. Carrillo and J. Rosado, A wellposedness theory in measures for some kinetic models of collective motion, Math. Models Methods Appl. Sci., 21 (2011), 515539. doi: 10.1142/S0218202511005131. Google Scholar 
[4] 
C. Canuto, F. Fagnani and P. Tilli, A Eulerian approach to the analysis of rendezvous algorithms, in "Proceedings of the 17th IFAC World Congress", (2008), 90399044. Google Scholar 
[5] 
E. Cristiani, P. Frasca and B. Piccoli, Effects of anisotropic interactions on the structure of animal groups, J. Math. Biol., 62 (2011), 569588. doi: 10.1007/s0028501003477. Google Scholar 
[6] 
E. Cristiani, B. Piccoli and A. Tosin, Modeling selforganization in pedestrian and animal groups from macroscopic and microscopic viewpoints, in "Mathematical Modeling of Collective Behavior in SocioEconomic and Life Sciences" (eds. G. Naldi, L. Pareschi and G. Toscani), Birkhäuser, Boston, (2010), 337364. Google Scholar 
[7] 
R. J. LeVeque, "Numerical Methods for Conservation Laws," 2^{nd} edition, Birkhäuser Verlag, Basel, 1992. Google Scholar 
[8] 
B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn., 21 (2009), 85107. doi: 10.1007/s001610090100x. Google Scholar 
[9] 
B. Piccoli and A. Tosin, Timeevolving measures and macroscopic modeling of pedestrian flow, Arch. Ration. Mech. Anal., 199 (2011), 707738. doi: 10.1007/s002050100366y. Google Scholar 
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