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 H01(0,π)×H-1(0,π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.