We study a damped semi-linear wave equation in a bounded domain
of R^3 with smooth boundary. It is proved that any H^2-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. This is a
joint work with Thomas Duyckaerts and Armen Shirikyan.