Advances in Differential Equations
- Adv. Differential Equations
- Volume 13, Number 11-12 (2008), 1051-1074.
Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions
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.
Adv. Differential Equations Volume 13, Number 11-12 (2008), 1051-1074.
First available in Project Euclid: 18 December 2012
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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