Attractors of semigroups associated with nonlinear systems for diffusive phase separation
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.
scientific article; zbMATH DE number 1370619