Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an ad hoc well-posedness theorem for systems of nonlocal conservation laws in several space dimensions interacting nonlocally with a system of ODEs. Numerical integrations show possible applications to the interaction of different groups of pedestrians and also with other agents.
Borsche, R., Colombo, R., Garavello, M., Meurer, A. (2015). Differential Equations Modeling Crowd Interactions. JOURNAL OF NONLINEAR SCIENCE, 25(4), 827-859 [10.1007/s00332-015-9242-0].
Differential Equations Modeling Crowd Interactions
GARAVELLO, MAURO;
2015
Abstract
Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an ad hoc well-posedness theorem for systems of nonlocal conservation laws in several space dimensions interacting nonlocally with a system of ODEs. Numerical integrations show possible applications to the interaction of different groups of pedestrians and also with other agents.
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