A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions

Abstract

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 contexts in several scientific fields. In this survey article, we briefly review the derivation, structure as well as some analytical issues for the Cahn-Hilliard equation and its variants. Our focus will be placed on the well-posedness and long-time behavior of the Cahn-Hilliard equation in the classical setting and recent progresses on the dynamic boundary conditions accounting for non-trivial boundary effects.

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Cited by in corpus (6)

• Two-phase flows with bulk-surface interaction: thermodynamically consistent Navier-Stokes-Cahn-Hilliard models with dynamic boundary conditions
• A Uniquely Solvable, Positivity-Preserving and Unconditionally Energy Stable Numerical Scheme for the Functionalized Cahn-Hilliard Equation with Logarithmic Potential
• Well-posedness of a bulk-surface convective Cahn--Hilliard system with dynamic boundary conditions
• Two-phase flows through porous media described by a Cahn--Hilliard--Brinkman model with dynamic boundary conditions
• A phase field model of Cahn-Hilliard type for tumour growth with mechanical effects and damage
• Well-posedness and long-time behavior of a bulk-surface Cahn--Hilliard model with non-degenerate mobility