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Presented here is a study of a viscoelastic wave equation with supercriticalsource and damping terms. We employ the theory of monotone operators andnonlinear semigroups, combined with energy methods to establish the existenceof a unique local weak solution. In addition, it is shown that the solutiondepends continuously on the initial data and is global provided the dampingdominates the source in an appropriate sense.

Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping