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 …

In this paper we present and analyze finite difference numerical schemes for the Cahn-
Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second …

The energy dissipation law and the maximum bound principle (MBP) are two important
physical features of the well-known Allen--Cahn equation. While some commonly used first …

In this paper we propose and analyze a finite difference numerical scheme for the Poisson-
Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP …

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}} …

This paper is concerned with the generalized Allen–Cahn equation with a nonlinear mobility
that may be degenerate, which also includes an advection term appearing in many …

We introduce a fractional variant of the Cahn–Hilliard equation settled in a bounded domain
Ω⊂ RN and complemented with homogeneous Dirichlet boundary conditions of solid type …

Abstract The Cahn–Hilliard equation is a fundamental model that describes phase
separation processes of binary mixtures. In recent years, several types of dynamic boundary …

We consider the so-called Cahn–Hilliard–Oono equation with singular (eg logarithmic)
potential in a bounded domain of ℝ d, d≤ 3. The equation is subject to an initial condition …