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In this paper we consider the weak viscoelastic equation with an internal time-varying delay term in a bounded domain. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general decay rate estimate for the energy, which depends on the behavior of both α and g.

GENERAL DECAY RATE ESTIMATE FOR THE ENERGY OF A WEAK VISCOELASTIC EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM