In this paper we give an overview of some recent results concerning partial differential equations modeling collective movements, namely, vehicular traffic flows and crowds dynamics. The focus is on traveling-wave solutions to degenerate parabolic equations in one space dimension, even if we briefly discuss models based on different equations. The case of networks is also taken into consideration. The parabolic degeneration opens the possibilities of several different behaviors of the traveling-wave solutions, which are investigated in details.
Wavefronts in Traffic Flows and Crowds Dynamics / Corli, Andrea; Malaguti, Luisa. - 43:(2021), pp. 167-189. [10.1007/978-3-030-61346-4_8]
Wavefronts in Traffic Flows and Crowds Dynamics
Malaguti, Luisa
2021
Abstract
In this paper we give an overview of some recent results concerning partial differential equations modeling collective movements, namely, vehicular traffic flows and crowds dynamics. The focus is on traveling-wave solutions to degenerate parabolic equations in one space dimension, even if we briefly discuss models based on different equations. The case of networks is also taken into consideration. The parabolic degeneration opens the possibilities of several different behaviors of the traveling-wave solutions, which are investigated in details.
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