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2008 Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions
Stéphane Gerbi, Belkacem Said-Houari
Adv. Differential Equations 13(11-12): 1051-1074 (2008).

Abstract

In this paper we consider a multi-dimensional damped semilinear wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. We firstly prove the local existence by using the Faedo-Galerkin approximations combined with a contraction mapping theorem. Secondly, the exponential growth of the energy and the $L^p$ norm of the solution is presented.

Citation

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Stéphane Gerbi. Belkacem Said-Houari. "Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions." Adv. Differential Equations 13 (11-12) 1051 - 1074, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1183.35035
MathSciNet: MR2483130

Subjects:
Primary: 35L75
Secondary: 35B40, 35L35

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 11-12 • 2008
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