  We study a damped semi-linear wave equation in a bounded domain with smooth
boundary. It is proved that any sufficiently smooth solution can be stabilised
locally by a finite-dimensional feedback control supported by a given open
subset satisfying a geometric condition. The proof is based on an investigation
of the linearised equation, for which we construct a stabilising control
satisfying the required properties. We next prove that the same control
stabilises locally the non-linear problem.
