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

Abstract

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.