  We consider a model for the evolution of an interface in a heterogeneous
environment governed by a parabolic equation. The heterogeneity is introduced
as obstacles exerting a localized dry friction. Our main result establishes the
emergence of a rate-independent hysteresis for suitable randomly distributed
obstacles, i.e., interfaces are pinned by the obstacles until a certain
critical applied driving force is exceeded. The treatment of such a model in
the context of pinning and depinning requires a comparison principle. We prove
this property and hence the existence of viscosity solutions. Moreover, under
reasonable assumptions, we show that viscosity solutions are equivalent to weak
solutions.
