中文摘要：

本文主要研究带记忆项的强阻尼波方程δt^2u-△δtu-k（0）△u-∫0^∞k＇（s）△u（t-s）ds＋φ（u）=f,解的长时间行为．我们证明了轨道和全局吸引子的存在性，并给出了它们结构的刻画．

英文摘要：

In this paper, we study the following strongly damped wave equation with memory effect δt^2u-△δtu-k（0）△u-∫0^∞k＇（s）△u（t-s）ds＋φ（u）=f.Other than consider the problem in the history space setting as the previous works, we are concerned with the corresponding system acts in the space of initial data of the Cauchy problem. We will prove the existence of trajectory attractors and global at- tractors for the above equation. Moreover, we will state the results about the structure for the trajectory and global attractor of the equation.