| Summary: | In this paper, we study a three-dimensional (3D) viscoelastic wave equation with nonlinear weak damping, supercritical sources and prescribed past history (Formula presented.), (Formula presented.): (Formula presented.) where the relaxation function k is monotone decreasing with (Formula presented.), (Formula presented.) and (Formula presented.). When the source is stronger than dissipations, i.e. (Formula presented.), we obtain some finite time blow-up results with positive initial energy. In particular, we obtain the existence of certain solutions which blow up in finite time for initial data at arbitrary energy level.
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