Pullback attractor for a non-autonomous modified Swift–Hohenberg equation

This paper is concerned with a non-autonomous modified Swift–Hohenberg equation ut+Δ2u+2Δu+au+b|∇u|2+u3=g(x,t)ut+Δ2u+2Δu+au+b|∇u|2+u3=g(x,t). It is shown that a pullback attractor exists when its external force has exponential growth. Due to the nonlinear terms b|∇u|2b|∇u|2 and u3u3, the estimates are delicate. We overcome this difficulty by imposing the exponential growth condition on the external forcing term g(x,t)g(x,t).