Consider radial solutions of the wave equation outside a ball in 3 space dimensions with Dirichlet boundary conditions, and a focusing superquintic nonlinearity. This equation has a countable family of stationary solutions. I will prove that any global solution converges, up to a dispersive term, to one of the stationary solutions. This is in sharp contrast with the case without obstacle, for which there is no stationary solution and any bounded global solution scatters to a linear solution.

This is a joint work with Jianwei Yang.