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We are concerned with the well-posedness of solutions as well as the asymptotic behaviour of the energy related to the viscoelastic wave equation with localized memory with past history and supercritical source and damping terms, posed on a bounded domain Ω ⊂ R 3 . Avoiding any relation between the damping and source terms, we obtain the global existence of solutions and the uniform energy decay rates, introducing the notion of a potential well and defining the expanded total energy functional. We also prove that weak solutions blow-up in finite time. [ABSTRACT FROM AUTHOR]