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Surface diffusion with triple junctions: A stability criterion for stationary solutions
Garcke, Harald, 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.Date of publication of this fulltext: 24 Mar 2010 06:46
Article
DOI to cite this document: 10.5283/epub.13768
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. ...
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.
Involved Institutions
Details
| Item type | Article | ||||||||||||
| Journal or Publication Title | Advances in Differential Equations | ||||||||||||
| Place of Publication: | Regensburg | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Series of the University of Regensburg: | Preprintreihe der Fakultät Mathematik | ||||||||||||
| Volume: | 15 | ||||||||||||
| Number of Issue or Book Chapter: | 5-6 | ||||||||||||
| Page Range: | pp. 437-472 | ||||||||||||
| Date | 2010 | ||||||||||||
| Institutions | Mathematics > Prof. Dr. Harald Garcke | ||||||||||||
| Classification |
| ||||||||||||
| Keywords | fourth order geometric evolution problem, surface diffusion, network of curves, linearized stability, Poincar´e inequality on a network, H−1-gradient flow | ||||||||||||
| Dewey Decimal Classification | 500 Science > 510 Mathematics | ||||||||||||
| Status | Published | ||||||||||||
| Refereed | Yes, this version has been refereed | ||||||||||||
| Created at the University of Regensburg | Partially | ||||||||||||
| URN of the UB Regensburg | urn:nbn:de:bvb:355-epub-137688 | ||||||||||||
| Item ID | 13768 |
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