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 and some of its variants Home 8.{{subColumn.name}} AIMS
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In this paper we propose and analyze a weakly nonlinear, energy stable numerical scheme
for the strongly anisotropic Cahn-Hilliard model. In particular, a highly nonlinear and …

We develop efficient energy stable numerical methods for solving isotropic and strongly
anisotropic Cahn–Hilliard systems with the Willmore regularization. The scheme, which …

Computing equilibrium shapes of crystals (ESCs) is a challenging problem in materials
science that involves minimizing an orientation-dependent (ie, anisotropic) surface energy …

We consider an initial‐boundary value problem of a square phase‐field crystal (SPFC)
model, which is a nonlinear parabolic equation of sixth‐order. The model is a variant of the …

Abstract We consider a Cahn–Hilliard equation in a bounded domain Ω in ℝ n over a time
interval (0, T) and discuss the backward problem in time of determining intermediate data …

We propose and analyze a second order accurate in time, energy stable numerical scheme
for the strongly anisotropic Cahn–Hilliard system, in which a biharmonic regularization has …

In this paper, the well posedness of a sixth-order phase-field equation with degenerate
phase-dependent diffusion mobility in three-dimensional space is studied. We first define a …

We consider the viscous Allen-Cahn and Cahn-Hilliard models with an additional term
called the nonlinear Willmore regularization. First, we are interested in the well-posedness …