  In this paper we investigate the stationary profiles of a nonlinear
Fokker-Planck equation with small diffusion and nonlinear in- and outflow
boundary conditions. We consider corridors with a bottleneck whose width has a
global nondegenerate minimum in the interior. In the small diffusion limit the
profiles are obtained constructively by using methods from geometric singular
perturbation theory (GSPT). We identify three main types of profiles
corresponding to: (i) high density in the domain and a boundary layer at the
entrance, (ii) low density in the domain and a boundary layer at the exit, and
(iii) transitions from high density to low density inside the bottleneck with
boundary layers at the entrance and exit. Interestingly, solutions of the last
type involve canard solutions generated at the narrowest point of the
bottleneck. We obtain a detailed bifurcation diagram of these solutions in
terms of the in- and outflow rates. The analytic results based on GSPT are
further corroborated by computational experiments investigating corridors with
bottlenecks of variable width.
