Global Attractor for the Cahn–Hilliard System with Fast Growing Nonlinearity

For N=1, the system reduces to the original Cahn Hilliard model describing decomposition of a binary alloy which has been studied by many authors (for instance, see [1, 3, 4, 9, 11]). In general, it is proposed as a phase separation model in the case where the alloy consists of N+1 components. The derivation of (1.1) (1.4) as well as many theoretical results concerning this problem can be found, for example, in [5, 6]. More recently, Cholewa and Dlotko [2] investigated the dynamical properties of (1.1) (1.4). They proved that the system possesses global attractors on some affined subspaces of [H(0)] under the assumptions: