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In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non-uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.
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Kaïs Ammari, Ahmed Bchatnia, Karim El Mufti, Non-Uniform Decay of the Energy of some Dissipative Evolution Systems. Z. Anal. Anwend. 36 (2017), no. 2, pp. 239–251DOI 10.4171/ZAA/1587