Strongly damped wave equation with exponential nonlinearities

In this paper, we study the initial boundary value problem for two-dimensional strongly 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 ( Ω ) ∩ L ∞ ( Ω ) ) × L 2 ( Ω ) .