Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain (Q1869767)

The paper focuses on a mixed problem in an exterior domain for the linear dissipative wave equation with localized disspation. In case of non-local dissipation, i.e. the coefficient of the dissipative term is \(a(x)=1\), decay estimates for weighted initial data have been reported by \textit{R. Ikehata} and \textit{T. Matsuyama} in [Sci. Math. Jap. 55, 33-42 (2002; Zbl 1005.35020)] and by \textit{A. Saeki} and \textit{R. Ikehata} in [SUT J. Math. 36, 267-277 (2000; Zbl 1158.35327)]. The aim of the present paper is to obtain fast decay estimates for the stated problem with weighted initial data and a localized dissipation.