Feedback stabilization along a path of steady-states for 1-D semilinear heat and wave equations

We report the problem of feedback stabilization along a path of steady-states, and of exact boundary controllability of semilinear one-dimensional heat and wave equations, investigated in [5], [6]. The main result is that it is possible to move from any steady-state to any other one by means of a boundary control, provided that they are in the same connected component of the set of steady-states. The proof is based on an effective feedback stabilization procedure which is efficiently implementable.