An overview will be given of some nonlinear parabolic-like evolution problems which are off
the classical beaten track, but have increased in importance during the past decade. The …

This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

A phase field model for the mixture of two incompressible fluids is presented in this paper.
The model is based on an energetic variational formulation. It consists of a Navier–Stokes …

We prove that level surfaces of solutions to the Cahn-Hilliard equation tend to solutions of
the Hele-Shaw problem under the assumption that classical solutions of the latter exist. The …

This review concerns the computation of curvature-dependent interface motion governed by
geometric partial differential equations. The canonical problem of mean curvature flow is that …

We propose and analyze a semi-discrete (in time) scheme and a fully discrete scheme for
the Allen-Cahn equation ut− Δ u+ ɛ− 2 f (u)= 0 arising from phase transition in materials …

In this paper we present an unconditionally solvable and energy stable second order
numerical scheme for the three-dimensional (3D) Cahn–Hilliard (CH) equation. The scheme …

We propose and analyze a semi-discrete and a fully discrete mixed finite element method for
the Cahn-Hilliard equation ut+ Δ (ɛ Δ u− ɛ− 1 f (u))= 0, where ɛ> 0 is a small parameter …

GLOBAL ASYMPTOTIC LIMIT OF SOLUTIONS OF THE CAHN-HILLIARD EQUATION XINFU
CHEN Abstract 1. Introduction lkuE = l ί ^ = > (x Page 1 J. DIFFERENTIAL GEOMETRY Vol. 44 …

We consider the distinguished limits of the phase field equations and prove that the
corresponding free boundary problem is attained in each case. These include the classical …