Boundary Stabilization of Equilibrium Solutions to Parabolic Equations

In this note, a stabilizing feedback boundary controller for the equilibrium solutions to parabolic equations with Dirichlet boundary control is designed. The feedback controller is expressed in terms of the eigenfunctions φ_j corresponding to unstable eigenvalues {λ_j}j=1^N of the linearized equation. For d=1, this stabilizing procedure is applicable for N=1 only, while for d > 1 it is of conditional nature requiring the independence of ∂φ_j/∂_n on the part of the boundary where the control is applied.