We study a Cahn-Hilliard-Hele-Shaw (or Cahn-Hilliard-Darcy) system for an incompressible mixture of two fluids. The relative concentration difference $\varphi$ is governed by convective nonlocal Cahn-Hilliard equation with degenerate mobility and logarithmic potential. volume averaged fluid velocity $\mathbf{u}$ obeys Darcy's law depending on the so-called Korteweg force $\mu\nabla \varphi$, wh...

The Cahn-Hilliard-Cook equation continues to be a useful model describing binary phase separation in systems such as alloys and other physical and chemical applications. We describe our investigation of this field equation and report on the various discretisation schemes we used to integrate the system in one-, twoand three-dimensions. We also discuss how the equation can be visualised effectiv...

An existence result for the Cahn{Hilliard equation with a concentration dependent diiusional mobility is presented. In particular the mobility is allowed to vanish when the scaled concentration takes the values 1 and it is shown that the solution is bounded by 1 in magnitude. Finally applications of our method to other degenerate fourth order parabolic equations are discussed.

We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in R, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature.

We consider a generalization of the Cahn-Hilliard equation that incorporates an elastic energy density which, being quasi-convex, incorporates micro-structure formation on smaller length scales. We explore the global existence of weak solutions in two and three dimensions. We compare theoretical predictions with experimental observations of coarsening in superalloys.

This article concerns a multi-dimensional Cahn-Hilliard equation subject to Neumann boundary condition. We show existence of the periodic solutions by using the viscosity approach. By applying the Schauder fixed point theorem, we show existence of the solutions to the suitable approximate problem and then obtain the solutions of the considered periodic problem using a priori estimates. Our resu...

This review explores the physical features of Cahn–Hilliard equation and how various thermodynamic models can be incorporated to study mixtures such as polymer blends.

We consider the singular limit of the Allen–Cahn type equation with a periodic nonlinear term. We obtain that several interfaces appear when the interface thickness parameter (denoted by ε) tends to 0. We also obtain that the interfaces move by the mean curvature flow with driving force term.