# American Institute of Mathematical Sciences

2009, 2009(Special): 60-71. doi: 10.3934/proc.2009.2009.60

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

 1 University of Nebraska-Lincoln, Lincoln, NC 68588-0130, United States 2 Department of Mathematics, University of Nebraska-Lincoln, Avery Hall 239, Lincoln, NE 68588

Received  June 2008 Revised  April 2009 Published  September 2009

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.
Citation: Lorena Bociu, Petronela Radu. Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping. Conference Publications, 2009, 2009 (Special) : 60-71. doi: 10.3934/proc.2009.2009.60
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