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.
"Local energy decay for some hyperbolic equations with initial data decaying slowly near infinity." Hokkaido Math. J. 36 (1) 53 - 71, February 2007. https://doi.org/10.14492/hokmj/1285766662