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 $$(H_{0}^{{1}(\Omega)\cap} L^{{\infty}(\Omega))\times} L<sup>{2}(\Omega)$$.