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In this paper, we consider a transmission problem in a bounded domain with aviscoelastic term and a delay term. Under appropriate hypothesis on therelaxation function and the relationship between the weight of the damping andthe weight of the delay, we prove the well-posedness result by usingFaedo-Galerkin method. By introducing suitable Lyaponov functionals, weestablish a general decay result, from which the exponential and polynomialtypes of decay are only special cases.

Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay