Surface diffusion with triple junctions: A stability criterion for stationary solutions
type: Item
instance of: scholarly article
title: Surface diffusion with triple junctions: A stability criterion for stationary solutions
zbMATH Open document ID: 1228.35042
author: Harald Garcke
author: Kazuo Ito
author: Yoshihito Kohsaka
published in: Advances in Differential Equations
publication date: 2010-07-09T00:00:00Z
review text: The authors consider a fourth-order geometric flow on a network of curves in a bounded domain \(\Omega\). This flow decreases a weighted total length of the curves and preserves the enclosed volumes. They first formulate the geometric evolution problem as an appropriate PDE problem and give a Poincaré-style estimate on a network of curves. And then, in this paper, the authors study the linearized stability of stationary solutions, using the \(H^{-1}\)-gradient flow structure of the problem, and show that the stationary solutions of this flow are critical points of a partition problem in \(\Omega\).
reviewed by: Shengliang Pan
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 35K35
zbMATH DE Number: 5734997
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5734997