Local energy decay for a class of hyperbolic equations with constant coefficients near infinity

Abstract

A uniform local energy decay result is derived to a compactly perturbed hyperbolic equation with spatial vari¬able coefficients. We shall deal with this equation in an N -dimensional exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data and the equation includes anisotropic variable coefficients {ai(x): i = 1, 2, …, N }, which are not necessarily equal to each other (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)