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

Lorena Bociu; Petronela Radu

doi:10.3934/proc.2009.2009.60

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2009, Volume 2009: 60-71. Doi: 10.3934/proc.2009.2009.60 open access

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

Lorena Bociu^1, and
Petronela Radu^2,

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

Received: June 2008

Revised: April 2009

Published: August 2009

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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.

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Mathematics Subject Classification: Primary: 35L15, 35L70; Secondary: 35L05.

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