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

Pages: 60 - 71, Issue Special, September 2009

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Lorena Bociu - University of Nebraska-Lincoln, Lincoln, NC 68588-0130, United States (email)
Petronela Radu - Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, 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
Mathematics Subject Classification:  Primary: 35L15, 35L70; Secondary: 35L05

Received: June 2008;      Revised: April 2009;      Published: September 2009.