This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

The Cahn-Hilliard equation is a fundamental model that describes the phase separation
process in multi-component mixtures. It has been successfully extended to many different …

We consider the nonlocal Cahn-Hilliard equation with singular (logarithmic) potential and
constant mobility in three-dimensional bounded domains and we establish the validity of the …

We study the separation property for Cahn-Hilliard type equations with constant mobility and
(physically relevant) singular potentials in two dimensions. That is, any solution with initial …

We study a diffuse interface model that describes the dynamics of incompressible two-phase
flows with chemotaxis effects. This model also takes into account some significant …

We investigate the nonlocal version of the Abels-Garcke-Grün (AGG) system, which
describes the motion of a mixture of two viscous incompressible fluids. This consists of the …

We study an initial-boundary value problem for the incompressible Navier–Stokes–Cahn–
Hilliard system with non-constant density proposed by Abels, Garcke and Grün in 2012. This …

We consider a nonlinear system which consists of the incompressible Navier–Stokes
equations coupled with a convective nonlocal Cahn–Hilliard equation. This is a diffuse …

The paper is concerned with the analysis of a popular convex-splitting finite element method
(FEM) for the Cahn–Hilliard–Navier–Stokes system, which has been widely used in practice …

In this paper, we analyze a general diffuse interface model for incompressible two-phase
flows with unmatched densities in a smooth bounded domain Ω ⊂ R^ d Ω⊂ R d (d= 2, 3 d …