Advances in Differential Equations

Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions

Stéphane Gerbi and Belkacem Said-Houari

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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.

Article information

Source
Adv. Differential Equations, Volume 13, Number 11-12 (2008), 1051-1074.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867286

Mathematical Reviews number (MathSciNet)
MR2483130

Zentralblatt MATH identifier
1183.35035

Subjects
Primary: 35L75: Nonlinear higher-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35L35: Initial-boundary value problems for higher-order hyperbolic equations

Citation

Gerbi, Stéphane; Said-Houari, Belkacem. Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions. Adv. Differential Equations 13 (2008), no. 11-12, 1051--1074. https://projecteuclid.org/euclid.ade/1355867286


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