Motion of Islands of Elastic Thin Films in the Dewetting Regime

TL;DR

This paper develops a mathematical model for the motion of elastic thin film islands during dewetting, incorporating moving contact lines and establishing short-time existence of solutions.

Contribution

It introduces a variational model with surface energies for solid-state dewetting, addressing the complex dynamics of moving contact lines in thin films.

Findings

Established short-time existence for the evolution law.

Extended the model to include moving contact lines.

Analyzed the surface diffusion evolution with curvature regularization.

Abstract

This paper addresses a two-dimensional sharp interface variational model for solid-state dewetting of thin films with surface energies, introduced by Wang, Jiang, Bao, and Srolovitz in \cite{jiang2016solid}. Using the $H^{-1}$-gradient flow structure of the evolution law, short-time existence for a surface diffusion evolution equation with curvature regularization is established in the context of epitaxially strained two-dimensional films. The main novelty, as compared to the study of the wetting regime, is the presence of moving contact lines.