Continuous dependence of attractors on the shape of domain

Let $\Omega_0$ be a bounded domain in $\mathbb R^n$, let $\mathcal G$ be a family of diffeomorphisms, and let $\Omega_G=G(\Omega_0)$ for $G\in\mathcal G$. Denote by $\Sigma_t(G)$ the semigroup generated by a fixed parabolic PDE with Dirichlet boundary conditions on the boundary of $\Omega_G$. Let $A_G$ be the global attractor $\Sigma_t(G)$. Conditions are given under which a generic diffeomorphism $G\in\mathcal G$ is a continuity point of the map $G\mapsto A_G$. Bibliography: 12 titles.