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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174064In 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.12 pages, 1 figureAnalysis of PDEs35L15; 35L70; 35L05Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and dampingtext