Local energy decay for some hyperbolic equations with initial data decaying slowly near infinity

Abstract

A uniform local energy decay property is discussed to a linear hyperbolic equation with spatial variable coefficients. We shall deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we assume algebraic order weight restrictions as $\vert x\vert \to +\infty$ on the initial data in order to derive the uniform local energy decay, and its proof is quite simple.