Attractors of semigroups associated with nonlinear systems for diffusive phase separation. (1996) - Kenmochi, Nobuyuki
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.