Variational models for phase separation

Models for phase separation and their mathematics ∗

The gradient flow approach to the Cahn-Hilliard and phase field models is developed, and some basic mathematical properties of the models, especially phase separation phenomena, are reviewed.

Variational models for phase transitions An approach via Γ-convergence

This paper is an extended version of the lecture delivered at the Summer School on Differential Equations and Calculus of Variations (Pisa, September 16-28, 1996). That lecture was conceived as an introduction to the theory of Γ-convergence and in particular to the Modica-Mortola theorem; I have tried to reply the style and the structure of the lecture also in the written version. Thus first co...

Modified models of polymer phase separation.

In this paper we discuss continuum models of phase separation in polymer solutions, with emphasis on the thermodynamic foundation of these models. We demand that these models obey a free energy dissipation relation, which in the present context plays the role of the second law of thermodynamics, since the system is isothermal. First, we derive a modified two-fluid model for viscoelastic phase s...

Coarsening rates for models of multicomponent phase separation

We study the coarsening of solutions of two models of multicomponent phase separation. One is a constant mobility system; the other is a degenerate mobility system. These models are natural generalizations of the Cahn-Hilliard equation to the case of a vector-valued order parameter. It has been conjectured that the characteristic length scale `(t) grows like t as t→∞ for the first case and ` ∼ ...

On Mathematical Models for Phase Separation in Elastically Stressed Solids