Local energy decay for linear wave equations with non-compactly supported initial data

摘要

A local energy decay problem is studied to a typical linear wave equation in an exterior domain. For this purpose, we do not assume any compactness of the support on the initial data. This generalizes a previous famous result due to Morawetz (Comm. Pure Appl. Math. 1961; 14:561-568). In order to prove local energy decay we mainly apply two types of new ideas due to Ikehata-Matsuyama (Sci. Math. Japon. 2002; 55:33-42) and Todorova-Yordanov (J. Differential Equations 2001; 174:464). Copyright (C) 2004 John Wiley Sons, Ltd.