  We analyze the dynamics of the flow generated by a nonlinear parabolic
problem when some reaction and potential terms are concentrated in a
neighborhood of the boundary. We assume that this neighborhood shrinks to the
boundary as a parameter \epsilon goes to zero. Also, we suppose that the "inner
boundary" of this neighborhood presents a highly oscillatory behavior. Our main
goal here is to show the continuity of the family of attractors with respect to
\epsilon. Indeed, we prove upper semicontinuity under the usual properties of
regularity and dissipativeness and, assuming hyperbolicity of the equilibria,
we also show the lower semicontinuity of the attractors at \epsilon=0.
