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 involves fourth-order spatial derivatives. Finite element
solutions are not common because primal variational formulations of fourth-order operators …

In this paper we develop an evolution of the C^1 virtual elements of minimal degree for the
approximation of the Cahn--Hilliard equation. The proposed method has the advantage of …

We introduce provably unconditionally stable mixed variational methods for phase-field
models. Our formulation is based on a mixed finite element method for space discretization …

Our aim in this article is to discuss recent issues related with the Cahn-Hilliard equation in
phase separation with the thermodynamically relevant logarithmic potentials; in particular …

We review physical, mathematical, and numerical derivations of the binary Cahn–Hilliard
equation (after John W. Cahn and John E. Hilliard). The phase separation is described by …

We formulate a unified framework of balance laws and thermodynamically-consistent
constitutive equations which couple Cahn–Hilliard-type species diffusion with large elastic …

The Cahn–Hilliard equation and some of its variants Home 8.{{subColumn.name}} AIMS
Mathematics Search Advanced Home {{newsColumn.name}} 1.{{subColumn.name}} {{newsColumn.name}} …

We present an efficient numerical framework for analyzing spinodal decomposition
described by the Cahn–Hilliard equation. We focus on the analysis of various implicit time …

Phase-field modeling is emerging as a promising tool for the treatment of problems with
interfaces. The classical description of interface problems requires the numerical solution of …