Attractors of semigroups associated with nonlinear systems for diffusive phase separation. (English) Zbl 0933.35189

Kenmochi, Nobuyuki

Abstr. Appl. Anal. 1, No. 2, 169-192 (1996).

Summary: 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 absolute temperature \(\theta:=\theta(t,x)\) 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 \(\sigma_*\leq w\leq\sigma^*\) (i.e., \(\sigma_*\) and \(\sigma^*\) 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 to construct its global attractor.

MSC:

35Q72	Other PDE from mechanics (MSC2000)
37L20	Symmetries of infinite-dimensional dissipative dynamical systems
35R35	Free boundary problems for PDEs
82C26	Dynamic and nonequilibrium phase transitions (general) in statistical mechanics

Keywords:

model for diffusive phase transitions; binary mixture; semigroup; global attractor