Abstract
We consider the nonautonomous modified Swift-Hohenberg equation
$$u_t+\Delta^2u+2\Delta
u+au+b|\nabla u|^2+u^3=g(t,x)$$
on a bounded smooth domain
$\Omega\subset\R^n$
with $n\leqslant 3$. We show that, if
$|b|<4$ and the external force $g$
satisfies some appropriate assumption, then the associated process has a
unique pullback attractor in the Sobolev space
$H_0^2(\Omega)$. Based on this existence, we
further prove the existence of a family of invariant Borel probability
measures and a statistical solution for this equation.