  The aim of this work is to design an explicit finite dimensional boundary
feedback controller of sampled-data form for locally exponentially stabilizing
the equilibrium solutions to semilinear parabolic equations. The feedback
controller is expressed in terms of the eigenfunctions corresponding to
unstable eigenvalues of the linearized equation. This stabilizing procedure is
applicable for any sampling rate, not necessary to be small enough, and it
tends to the continuous-times version when the sampling period tends to zero.
