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General constrained conservation laws. Application to pedestrian flow modeling

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  • We extend the results on conservation laws with local flux constraint obtained in [2, 12] to general (non-concave) flux functions and non-classical solutions arising in pedestrian flow modeling [15]. We first provide a well-posedness result based on wave-front tracking approximations and the Kružhkov doubling of variable technique for a general conservation law with constrained flux. This provides a sound basis for dealing with non-classical solutions accounting for panic states in the pedestrian flow model introduced by Colombo and Rosini [15]. In particular, flux constraints are used here to model the presence of doors and obstacles. We propose a "front-tracking" finite volume scheme allowing to sharply capture classical and non-classical discontinuities. Numerical simulations illustrating the Braess paradox are presented as validation of the method.
    Mathematics Subject Classification: Primary: 35L65; Secondary: 90B20.

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