  In the present contribution, a feedback control law is studied for a
quasilinear parabolic equation. First, we prove the well-posedness and some
regularity results for the Cauchy-Neumann problem for this equation, modified
by adding an extra term which is a multiple of the subdifferential of the
distance function from a closed convex set of the space of square-integrable
functions. Then, we consider convex sets of obstacle or double-obstacle type
and prove rigorously the following property: if the factor in front of the
feedback control is sufficiently large, then the solution reaches the convex
set within a finite time and then moves inside it.
