We consider several macroscopic models, based on systems of conservation laws, for the study of crowd dynamics. All the systems considered here contain nonlocal terms, usually obtained through convolutions with smooth functions, used to reproduce the visual horizon of each individual. We classify the various models according to the physical domain (the whole space ℝN or a bounded subset), to the terms affected by the nonlocal operators, and to the number of different populations we aim to describe. For all these systems, we present the basic well posedness and stability results.
Colombo, R., Lecureux-Mercier, M., Garavello, M. (2020). Crowd Dynamics Through Conservation Laws. In L. Gibelli (a cura di), Crowd Dynamics, Volume 2. Theory, Models, and Applications (pp. 83-110). Basel : Birkhauser [10.1007/978-3-030-50450-2_5].
Crowd Dynamics Through Conservation Laws
Garavello, M
2020
Abstract
We consider several macroscopic models, based on systems of conservation laws, for the study of crowd dynamics. All the systems considered here contain nonlocal terms, usually obtained through convolutions with smooth functions, used to reproduce the visual horizon of each individual. We classify the various models according to the physical domain (the whole space ℝN or a bounded subset), to the terms affected by the nonlocal operators, and to the number of different populations we aim to describe. For all these systems, we present the basic well posedness and stability results.
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