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

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

2008-11-13

arxiv.org/abs/0811.2151v1

Mathematics

Analysis of PDEs

12 pages, 1 figure

Scientific paper

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.

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