  The aim of this work is to design an explicit finite dimensional boundary
feedback controller for locally exponentially stabilizing the equilibrium
solutions to Fisher's equation in both $L^2(0,1)$ and $H^1(0,1)$. 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 level of instability, which extends the result of \cite{02}
for nonlinear parabolic equations. The effectiveness of the approach is
illustrated by a numerical simulation.
