Pullback attractors for a semilinear heat equation on time-varying domains

The existence of a pullback attractor is established for the nonautonomous dynamical system generated by the weak solutions of a semilinear heat equation on time-varying domains with homogeneous Dirichlet boundary conditions. It is assumed that the spatial domains Ot in RN are obtained from a bounded base domain O by a C2-diffeomorphism, which is continuously differentiable in the time variable, and are contained, in the past, in a common bounded domain.