  We analyze a nonlinear degenerate parabolic problem whose diffusion
coefficient is the Heaviside function of the distance of the solution itself
from a given target function. We show that this model behaves as an evolutive
variational inequality having the target as an obstacle: under suitable
hypotheses, starting from an initial state above the target the solution
evolves in time towards an asymptotic solution, eventually getting in contact
with part of the target itself. We also study a finite difference approach to
the solution of this problem, using the exact Heaviside function or a regular
approximation of it, showing the results of some numerical tests.
