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Abstract and Applied Analysis
Volume 1, Issue 2, Pages 169-192

Attractors of semigroups associated with nonlinear systems for diffusive phase separation

Department of Mathematics, Faculty of Education, Chiba University, Inageku, Chiba 263, Japan

Received 23 May 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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*wσ* (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.