Uniform decay rates for second-order hyperbolic equations with variable coefficients

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In this paper, we consider a second-order hyperbolic equations with variable coefficients and linear lower-order term. We use a new main multiplier and a suitable nonlinear version of a compactness uniqueness argument (Acta. Math. Sin. - Engl. Ser. 20(6) (2004), 1057-1072) to obtain the exponential stabilization of this system where no condition of smallness is needed.