Lorena Bociu - University of Nebraska-Lincoln, Lincoln, NC 68588-0130, United States (email)
Abstract: 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.
Keywords: wave equations, damping and source terms, weak solutions, energy identity
Received: June 2008; Revised: April 2009; Published: September 2009.