Strongly damped wave equation with exponential nonlinearities

Abstract

In this paper, we study the initial boundary value problem for the two dimensional strong damped wave equation with exponentially growing source and damping terms. We first show the well-posedness of this problem and then prove the existence of the global attractor in $(H_{0}^{1}(\Omega)\cap L^{\infty}(\Omega))\times L^{2}(\Omega)$.