The evolving surface Cahn-Hilliard equation with a degenerate mobility

TL;DR

This paper investigates the existence and uniqueness of weak and strong solutions to the Cahn-Hilliard equation with degenerate and positive mobility functions on evolving surfaces, advancing mathematical understanding of phase separation models.

Contribution

It establishes existence results and weak-strong uniqueness for the Cahn-Hilliard equation with degenerate and positive mobility on evolving surfaces.

Findings

Proved existence of weak solutions for degenerate mobility

Established weak-strong uniqueness when mobility is positive

Achieved uniqueness results under specific initial data conditions

Abstract

We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-strong uniqueness for the case of a positive mobility function, and under some further assumptions on the initial data we show uniqueness for a class of strong solutions for a degenerate mobility function.