Garcke, Harald and Kohsaka, Yoshihito and Sevcovic, Daniel (2009) Nonlinear stability of stationary solutions for curvature flow with triple junction. HOKKAIDO MATHEMATICAL JOURNAL, 38 (4). pp. 721-769. ISSN 0385-4035,
Full text not available from this repository. (Request a copy)Abstract
In this paper we analyze the motion of a network of three planar curves with a speed proportional to the curvature of the arcs, having perpendicular intersections with the outer boundary and a common intersection at a triple junction. As a main result we show that a linear stability criterion due to Ikota and Yanagida [13] is also sufficient for nonlinear stability. We also prove local and global existence of classical smooth solutions as well as Various energy estimates. Finally, we prove exponential stabilization of ail evolving network starting from the vicinity of a linearly stable stationary network.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PLANE-CURVES; BOUNDARY-CONDITIONS; SURFACE-DIFFUSION; EQUATION; EVOLUTION; NETWORKS; MOTION; curvature flow; triple junction; higher order estimates for the curvature; nonlinear stability of stationary solutions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 02 Sep 2020 08:42 |
| Last Modified: | 02 Sep 2020 08:42 |
| URI: | https://pred.uni-regensburg.de/id/eprint/28191 |
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