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

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  • In this paper we show existence of finite energy solutions for the Cauchy problem associated with a semilinear wave equation with interior damping and supercritical source terms. The main contribution consists in dealing with super-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 literature on nonlinear wave equations.
    Mathematics Subject Classification: Primary: 35L15, 35L70; Secondary: 35L05.

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