The linearized stability of stationary solutions for the surface diffusion flow with a triple junction is studied. We derive the second variation of the energy functional under the constraint that the enclosed areas are preserved and show a linearized stability criterion with the help of the -gradient flow structure of the evolution problem and the analysis of eigenvalues of a corresponding differential operator.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-5,
author = {Harald Garcke and Kazuo Ito and Yoshihito Kohsaka},
title = {Stability analysis of phase boundary motion by surface diffusion with triple junction},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {83-101},
zbl = {1178.35057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-5}
}
Harald Garcke; Kazuo Ito; Yoshihito Kohsaka. Stability analysis of phase boundary motion by surface diffusion with triple junction. Banach Center Publications, Tome 86 (2009) pp. 83-101. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-5/