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Nonlinear stability of stationary solutions for curvature flow with triple junction

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84050

Title: Nonlinear stability of stationary solutions for curvature flow with triple junction
Authors: Garcke, Harald Browse this author
Kohsaka, Yoshihito Browse this author
Sevcovic, Daniel Browse this author
Issue Date: 2008
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 900
Start Page: 1
End Page: 35
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 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 an evolving network starting from the vicinity of a linearly stable stationary network.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69708
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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