A Class of Non-Local Models for Pedestrian Traffic

Details A Class of Non-Local Models for Pedestrian Traffic A Class of Non-Local Models for Pedestrian Traffic

2011-04-15

arxiv.org/abs/1104.2985v2

Mathematics

Analysis of PDEs

Scientific paper

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Specific models are presented and their qualitative properties are shown through numerical integrations.

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