Global existence for semilinear wave equations in exterior domains

We consider exterior problems for linear and semilinear wave equations. We first derive total energy decay for the linear wave equation with a localized dissipation which is effective near infinity and critical part of the boundary. This can be applied to the proof of the global existence of finite energy or H₂ solutions for semilinear wave equations. Next, by use of the local energy decay: we show L^p estimates for the linear equations with a dissipation effective only near a part of the boundary and apply this again to the global existence of semilinear equations.