Abstract and Applied Analysis
Volume 1 (1996), Issue 2, Pages 169-192
doi:10.1155/S1085337596000085

Attractors of semigroups associated with nonlinear systems for diffusive phase separation

Abstract

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 θ:=θ(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 σ*≤w≤σ* (i.e., σ* and σ* 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.