  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 $p$-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 $p \to
\infty$, the weak solutions of the $p-$problem converge to a solution of the
congested crowd motion problem.
