Existence of nonclassical solutions in a Pedestrian flow model

The main result of this note is the existence of nonclassical solutions to the Cauchy problem for a conservation law modeling pedestrian flow. From the physical point of view, the main assumption of this model was recently experimentally confirmed in [D. Helbing, A. Johansson, H.Z. Al-Abideen, Dynamics of crowd disasters: An empirical study, Phys. Rev. E 75 (4) (2007) 046109]. Furthermore, the present model describes the fall in a door through-flow due to the rise of panic, as well as the Braess’ paradox. From the analytical point of view, this model is an example of a conservation law in which nonclassical solutions have a physical motivation and a global existence result for the Cauchy problem, with large data, is available.