Asymptotic For The Non-autonomous Weakly Dissipative Abstract Evolution Equations With Fading Memory

In this article, Based on the contractive function and the concept of pullback D-asymptotical compactness, and combining some new methods of energy estimate, we study the long-time behave for dynamical systems corresponding to the non-autonomous weakly dissipative abstract evolution equations with fading memory where Ω(?)R3 is a bounded domain with a smooth boundary.θ∈ (0,3/2), k(0), k(∞)> 0, and when s∈R+, k’(s)< 0. The main work are as follows:i)By using the contractive function, we obtain the existence of uniform attractor in Vθ×H×Lμ2(R; Vθ). The results are the improvements and extensions of the results of paper.ii)We prove the existence of pullback attractor by introducing a new function and applying the concept of pullback D-asymptotical compactness. The results are the improvements and extensions of the results of paper.