  We prove well-posedness results for the solution to an initial and
boundary-value problem for an Allen-Cahn type equation describing the
phenomenon of phase transitions for a material contained in a bounded and
regular domain. The dynamic boundary conditions for the order parameter have
been recently proposed by some physicists to account for interactions with the
walls. We show our results using suitable regularizations of the nonlinearities
of the problem and performing some a priori estimates which allow us to pass to
the limit thanks to compactness and monotonicity arguments.
