Global attractors for singular perturbations of the Cahn–Hilliard equations

We consider the singular perturbations of two boundary value problems, concerning respectively the viscous and the nonviscous Cahn–Hilliard equations in one dimension of space. We show that the dynamical systems generated by these two problems admit global attractors in the phase space , and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter