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 …

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

In this paper, we develop a series of efficient numerical schemes to solve the phase field
model for homopolymer blends. The governing system is derived from the energetic …

A new diffuse interface model for a two-phase flow of two incompressible fluids with different
densities is introduced using methods from rational continuum mechanics. The model fulfills …

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

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics is the first book to provide a systematic construction of exact …

We consider a phase field model for the formulation and solution of topology optimization
problems in the minimum compliance case. In this model, the optimal topology is obtained …

We present and analyze a second order in time variable step BDF2 numerical scheme for
the Cahn--Hilliard equation. The construction relies on a second order backward difference …

We show by using formal asymptotics that the zero level set of the solution to the Cahn–
Hilliard equation with a concentration dependent mobility approximates to lowest order in ɛ …