Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization

TL;DR

This paper proves short-time existence and analyzes stability for a surface diffusion evolution law with curvature regularization in 3D elastic films, using a minimizing movement scheme based on the $H^{-1}$-gradient flow.

Contribution

It establishes the existence, long-time behavior, and stability of solutions for a curvature-regularized surface diffusion model in three-dimensional elastic films.

Findings

Short-time existence of solutions is proved.

Long-time behavior and stability near flat configurations are analyzed.

The approach uses a minimizing movement scheme based on the $H^{-1}$-gradient flow.

Abstract

Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the $H^{-1}$-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a flat configuration are also addressed.