Non-linear Stability of Double Bubbles under Surface Diffusion
Analysis of PDEs
2019-10-08 v2
Abstract
We consider the evolution of triple junction clusters driven by the surface diffusion flow. On the triple line we use the boundary conditions derived by Garcke and Novick-Cohen as the singular limit of a Cahn-Hilliard equation with degenerated mobility. These conditions are the concurrency of the triple junction, angle conditions between the hypersurfaces, continuity of the chemical potentials and a flux-balance. For this system we show stability of its energy minimizers, i.e., standard double bubbles.The main argument relies on a Lojasiewicz-Simon gradient inequality. The proof of it differs from others works due to the fully non-linear boundary conditions and problems with the (non-local) tangential part.
Keywords
Cite
@article{arxiv.1910.01041,
title = {Non-linear Stability of Double Bubbles under Surface Diffusion},
author = {Harald Garcke and Michael Gößwein},
journal= {arXiv preprint arXiv:1910.01041},
year = {2019}
}