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

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.