Attractors of semigroups associated with nonlinear systems for diffusive phase separation. (1996)

• Record Type: Journal Article
• Authors: Kenmochi, Nobuyuki
• Is Part Of: Abstract and applied analysis. Volume 1:Number 2(1996)
• Page Start: 169
• Page End: 192
• Publication Date: 1996
• Subjects: System of parabolic equations -- diffusive phase separation -- semigroup -- attractor; Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337596000085
• Languages: English
• ISSNs: 1085-3375

Abstract

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 temperatureθ : = θ ( t, x ) and the order parameterw : = w ( t, x ), which are governed by a system of two nonlinear parabolic PDEs. The order parameterw is constrained to have double obstaclesσ * ≤ w ≤ σ * (i.e., σ * andσ * are the threshold values ofw ). The objective of this paper is to discuss the semigroup{ S ( t ) } associated with the phase separation model, and construct its global attractor.