Maximal Attractors for the m-Dimensional Cahn-Hilliard System

摘要

In this paper we discuss maximal attractors of the m-dimensional Cahn-Hilliard System in the product spaces (L^2(Ω))^m and (H^2(Ω))^m in terms of D.Henry's general theory and from the viewpoint of compactness and absorptivity of semigroups as R. Temam did. After giving the existence and uniqueness of global solutions, we technically restrict our discussion to some subspaces, give estimates with a new graph norm, and obtain the existence of maximal attractors and some properties of them.