Decay estimates for dissipative wave equations in exterior domains

Consider the initial boundary value problem for the linear dissipative wave equation ( +∂t )u = 0 in an exterior domain Ω ⊂ RN. Using the so-called cut-off method together with local energy decay and L2 decays in the whole space, we study decay estimates of the solutions. In particular, when N 3, we derive Lp decays with p 1 of the solutions. Next, as an application of the decay estimates for the linear equation, we consider the global solvability problem for the semilinear dissipative wave equations ( + ∂t )u = f (u) with f (u) = |u|α+1, |u|αu in an exterior domain.  2003 Elsevier Inc. All rights reserved.