Advances in Differential Equations

Surface diffusion with triple junctions: A stability criterion for stationary solutions

Harald Garcke, Kazuo Ito, and Yoshihito Kohsaka

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We study a fourth-order geometric evolution problem on a network of curves in a bounded domain $\Omega$. The flow decreases a weighted total length of the curves and preserves the enclosed volumes. Stationary solutions of the flow are critical points of a partition problem in $\Omega$. In this paper we study the linearized stability of stationary solutions using the $H^{-1}$-gradient flow structure of the problem. Important issues are the development of an appropriate PDE formulation of the geometric problem and Poincaré type estimate on a network of curves.

Article information

Adv. Differential Equations Volume 15, Number 5/6 (2010), 437-472.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B35: Stability 35G30: Boundary value problems for nonlinear higher-order equations 35K55: Nonlinear parabolic equations 35R35: Free boundary problems 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)


Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito. Surface diffusion with triple junctions: A stability criterion for stationary solutions. Adv. Differential Equations 15 (2010), no. 5/6, 437--472.

Export citation