Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data

Abstract

This paper is concerned with weighted energy estimates for solutions to wave equation [Formula: see text] with space-dependent damping term [Formula: see text] [Formula: see text] in an exterior domain [Formula: see text] having a smooth boundary. The main result asserts that the weighted energy estimates with weight function like polynomials are given and these decay rates are almost sharp, even when the initial data do not have compact support in [Formula: see text]. The crucial idea is to use special solution of [Formula: see text] including Kummer’s confluent hypergeometric functions.