General constrained conservation laws. Application to pedestrian flow modeling

Abstract

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.