Attractors for the Cahn–Hilliard equation with memory in 2D

We deal with the memory relaxation of the Cahn–Hilliard equation proposed by Rotstein et al. as a model for the phenomenological description of phase transition, which contains as a particular case the hyperbolic version of the equation. Due to the absence of viscosity effects, existence and uniqueness of solutions are far from being trivial in space dimension N>1N>1. This paper is devoted to the analysis of energy solutions for the 2D model. After discussing the well-posedness of the problem, we study its long-term dynamics and we prove the existence and regularity of the global attractor, provided that the relaxation parameter of the memory kernel is small enough.