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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," 2nd 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 well-posedness theory in measures for some kinetic models of collective motion, Math. Models Methods Appl. Sci., 21 (2011), 515-539.
doi: 10.1142/S0218202511005131. |
[4] |
C. Canuto, F. Fagnani and P. Tilli, A Eulerian approach to the analysis of rendez-vous algorithms, in "Proceedings of the 17th IFAC World Congress", (2008), 9039-9044. |
[5] |
E. Cristiani, P. Frasca and B. Piccoli, Effects of anisotropic interactions on the structure of animal groups, J. Math. Biol., 62 (2011), 569-588.
doi: 10.1007/s00285-010-0347-7. |
[6] |
E. Cristiani, B. Piccoli and A. Tosin, Modeling self-organization in pedestrian and animal groups from macroscopic and microscopic viewpoints, in "Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences" (eds. G. Naldi, L. Pareschi and G. Toscani), Birkhäuser, Boston, (2010), 337-364. |
[7] |
R. J. LeVeque, "Numerical Methods for Conservation Laws," 2nd edition, Birkhäuser Verlag, Basel, 1992. |
[8] |
B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn., 21 (2009), 85-107.
doi: 10.1007/s00161-009-0100-x. |
[9] |
B. Piccoli and A. Tosin, Time-evolving measures and macroscopic modeling of pedestrian flow, Arch. Ration. Mech. Anal., 199 (2011), 707-738.
doi: 10.1007/s00205-010-0366-y. |
show all references
References:
[1] |
L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," 2nd 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 well-posedness theory in measures for some kinetic models of collective motion, Math. Models Methods Appl. Sci., 21 (2011), 515-539.
doi: 10.1142/S0218202511005131. |
[4] |
C. Canuto, F. Fagnani and P. Tilli, A Eulerian approach to the analysis of rendez-vous algorithms, in "Proceedings of the 17th IFAC World Congress", (2008), 9039-9044. |
[5] |
E. Cristiani, P. Frasca and B. Piccoli, Effects of anisotropic interactions on the structure of animal groups, J. Math. Biol., 62 (2011), 569-588.
doi: 10.1007/s00285-010-0347-7. |
[6] |
E. Cristiani, B. Piccoli and A. Tosin, Modeling self-organization in pedestrian and animal groups from macroscopic and microscopic viewpoints, in "Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences" (eds. G. Naldi, L. Pareschi and G. Toscani), Birkhäuser, Boston, (2010), 337-364. |
[7] |
R. J. LeVeque, "Numerical Methods for Conservation Laws," 2nd edition, Birkhäuser Verlag, Basel, 1992. |
[8] |
B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn., 21 (2009), 85-107.
doi: 10.1007/s00161-009-0100-x. |
[9] |
B. Piccoli and A. Tosin, Time-evolving measures and macroscopic modeling of pedestrian flow, Arch. Ration. Mech. Anal., 199 (2011), 707-738.
doi: 10.1007/s00205-010-0366-y. |
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