We consider a model for diffusive phase transitions, for
instance, the component separation in a binary mixture. Our model is
described by two functions, the absolutete temperature $\theta :=\theta(t,x)$ and the order parameter $w := w(t,x)$ , which are governed by a
system of two nonlinear parabolic PDEs. The order parameter
$w$ is constrained to have double obstacles $\sigma_* \le w \le \sigma^*$ (i.e., $\sigma_*$ and $\sigma^*$ are the threshold values of $w$ ). The objective of this paper is to discuss the semigroup $\{S(t)\}$ associated with the phase separation model, and construct its global attractor.