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

Garcke, Harald and Ito, Kazuo and Kohsaka, Yoshihito (2010) Surface diffusion with triple junctions: A stability criterion for stationary solutions. Advances in Differential Equations 15 (5-6), pp. 437-472.

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Abstract

We study a fourth order geometric evolution problem on a network of curves
in a bounded domain
. 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
. 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 Poincar´e
type estimate on a network of curves.

Item Type:

Article

Institutions:

Mathematics > Prof. Dr. Harald Garcke

Classification:

Notation	Type
35B35	MSC
35G30	MSC
35K55	MSC
35R35	MSC
53C44	MSC

Keywords:

fourth order geometric evolution problem, surface diffusion, network of curves, linearized stability, Poincar´e inequality on a network, H−1-gradient flow

Subjects:

500 Science > 510 Mathematics

Status:

Published

Refereed:

Yes, this version has been refereed

Created at the University of Regensburg:

Partially

Owner:

Eva Ruetz

Deposited On:

24 Mar 2010 07:46