A granular model for crowd motion and pedestrian flow

Abstract We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele‐Shaw type equation involving a degenerate operator of ‐Laplacian type and a linear drift, for which we prove existence and uniqueness using nonlinear semigroup methods and the doubling variables technique. Our main result shows that, as , the weak solutions of the ‐problem converge to a solution of the congested crowd motion problem interpreted in a variational sense.