Well-posedness and long time behavior of a perturbed Cahn–Hilliard system with regular potentials

The aim of this paper is to study the well-posedness and long time behavior, in terms of finite-dimensional attractors, of a perturbed Cahn–Hilliard equation. This equation differs from the usual Cahn–Hilliard by the presence of the term ε(−Δu+f(u)). In particular, we prove the existence of a robust family of exponential attractors as ε goes to zero.