Time-dependent global attractor for extensible Berger equation

In this paper, we investigate the asymptotic behavior of the nonautonomous Berger equationε(t)utt+Δ2u−(Q+∫Ω|∇u|2dx)Δu+g(ut)+φ(u)=f,t>τ, on a bounded smooth domain Ω⊂RN with hinged boundary condition, where ε(t) is a decreasing function vanishing at infinity. Under suitable assumptions, we establish an invariant time-dependent global attractor within the theory of process on time-dependent space.