Time-dependent attractor of wave equations with nonlinear damping and linear memory

In this article, we consider the long-time behavior of solutions for the wave equation with nonlinear damping and linear memory. Within the theory of process on time-dependent spaces, we verify the process is asymptotically compact by using the contractive functions method, and then obtain the existence of the time-dependent attractor in array H¹₀(Ω)× L²(Ω)× L²μ(R⁺;H¹₀(Ω)) array .