Time-dependent asymptotic behavior of the solution for evolution equation with linear memory

In this article, by using the operator decomposition technique, we discuss the existence of a time-dependent global attractor for a nonlinear evolution equation with linear memory within the theory of time-dependent space. Furthermore, the regularity and asymptotic structure of the time-dependent attractor are proved, which means that the time-dependent attractor of the evolution equation converges to the attractor of the limit wave equation when the coefficient $ \varepsilon(t)\rightarrow0 $ as $ t\rightarrow \infty $.