In this paper we consider a multi-dimensional damped semiliear 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 Lp norm of the solution is presented.
@article{arxiv.0810.1013,
title = {Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions},
author = {Stéphane Gerbi and Belkacem Said-Houari},
journal= {arXiv preprint arXiv:0810.1013},
year = {2008}
}