Strong unique continuation for second-order hyperbolic equations with time-independent coefficients

In this paper we prove that if u is a solution to second-order hyperbolic equation $$\partial ^2_{t}u+a(x)\partial _{t}u-(\text { div}_x\left( A(x)\nabla _x u\right) +b(x)\cdot \nabla _x u+c(x)u)=0$$ and u is flat on a segment $$\{x_0\}\times (-T,T)$$ (T finite), then u vanishes in a neighborhood of $$\{x_0\}\times (-T,T)$$ . The novelty with respect to earlier papers on the subject is the nonvanishing damping coefficient a(x) in the hyperbolic equation.