Uniform decay estimates for the wave equation in an exterior domain

Abstract

The aim of this article is to establish a uniform pointwise decay estimate for the solution of the mixed problem for the linear wave equation in three space dimensions. We prove such an estimate by using the "cut-off method" as in the work of Shibata and Tsutsumi [23]. As an application, we treat the mixed problem for quadratically quasilinear wave equations exterior to a non-trapping obstacle.