Exponential attractors and inertial manifolds for singular perturbations of the Cahn–Hilliard equations

Abstract

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 exponential attractors and inertial manifolds in the phase space H 0 1(0, π)× H −1(0, π).