Radial conditions for global compact finite propagation for divergence-form elliptic operators

We study global compact finite propagation (GCFP) for the wave equation $u_{tt}=\operatorname{div}(A(x)\nabla u)$ on $\mathbb{R}^d$, that is, the property that a disturbance starting in a compact set cannot reach spatial infinity in finite time. For smooth strictly positive matrices $A$ we show that