摘要：The paper is concerned with the non-autonomous modified Swift-Hohenberg equation u t + △ 2 u + 2 △ u + a u + b ∇ u 2 + u 3 = g ( x , t ) $u_{t}+{\triangle }^,u+2{\triangle }u+au+b \nabla u ^,+u^"=g(x,t)$ . It is shown that a uniform attractor exists in H 0 2 $H_(^,$ when the external force only satisfies the translation bounded condition instead of translation compactness. In order to overcome the difficulty caused by the critical nonlinearity terms u 3 $u^"$ and the parameter b belonging to the real set R $\mathbb{R}$ , we take advantage of the Gagliardo-Nirenberg inequality several times.
