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In this paper we show existence of finite energy solutions for the Cauchyproblem associated with a semilinear wave equation with interior damping andsupercritical source terms. The main contribution consists in dealing withsuper-supercritical source terms (terms of the order of $|u|^p$ with $p\geq 5$in $n=3$ dimensions), an open and highly recognized problem in the literatureon nonlinear wave equations.

Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping