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.

Keywords

• System of parabolic equations
• diffusive phase separation
• semigroup
• attractor.