中文摘要：

讨论了带有线性记忆项和混合微分项的弱阻尼波方程解的长时间行为.证明了方程在非线性项满足临界增长条件下,在空间H_0-1（Ω）×L~2（Ω）×L_μ~2（R＋,R_0~1（Ω））中存在全局吸引子,其中半群的紧性通过压缩函数方法得到.

英文摘要：

This paper was concerned with the long-time behavior of the solutions for weakly damped wave equations with a mixed differential quotient term and linear memory. The existence of a global attractor in H（g2） x L（f2） x L2 （ E ＋, H（Ω）） was proven when the nonlinearity was allowed to have a cubic growth rate, referred to as the critical exponent. The asymptotic compact for the semigroup was witted via contrac- tive function.