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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:
[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. 
[2] 
N. Bellomo, "Modeling Complex Living Systems. A Kinetic Theory and Stochastic Game Approach," Birkhäuser, Boston, 2008. 
[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. 
[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. 
[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. 
[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. 
[7] 
R. J. LeVeque, "Numerical Methods for Conservation Laws," 2^{nd} edition, Birkhäuser Verlag, Basel, 1992. 
[8] 
B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn., 21 (2009), 85107. doi: 10.1007/s001610090100x. 
[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. 
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. 
[2] 
N. Bellomo, "Modeling Complex Living Systems. A Kinetic Theory and Stochastic Game Approach," Birkhäuser, Boston, 2008. 
[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. 
[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. 
[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. 
[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. 
[7] 
R. J. LeVeque, "Numerical Methods for Conservation Laws," 2^{nd} edition, Birkhäuser Verlag, Basel, 1992. 
[8] 
B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn., 21 (2009), 85107. doi: 10.1007/s001610090100x. 
[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. 
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