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 propose and analyze an energy stable numerical scheme for the Cahn–
Hilliard equation, with second order accuracy in time and the fourth order finite difference …

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}} …

In this paper, we consider the mathematical modeling and numerical approximation for the
fluid-surfactant phase field model coupled with the Navier–Stokes equations on surfaces …

In the realm of ecology, species naturally strive to enhance their own survival odds. This
study introduces and investigates a predator‐prey model incorporating reaction‐diffusion …

In this paper, we consider the numerical simulation of the binary fluid–surfactant phase field
model coupled with geometric curvature on the curved surface. By taking account of the …

This paper presents a general theory and isogeometric finite element implementation for
studying mass conserving phase transitions on deforming surfaces. The mathematical …

We develop an unconditionally stable direct discretization scheme for solving the phase-
field crystal equation on surfaces. The surface is discretized by using an unstructured …

Two semi-implicit numerical methods are proposed for solving the surface Allen-Cahn
equation which is a general mathematical model to describe phase separation on general …