Nonlinear stability of stationary solutions for curvature flow with triple junction

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dc.creatorGarcke, Harald
dc.creatorKohsaka, Yoshihito
dc.creatorSevcovic, Daniel
dc.date2008-02-21
dc.date.accessioned2026-07-07T09:22:17Z
dc.date.available2026-07-07T09:22:17Z
dc.descriptionIn 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.
dc.descriptionsubmitted
dc.identifierhttps://arxiv.org/abs/0802.3036
dc.identifierhttp://arxiv.org/abs/0802.3036
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155325
dc.subjectDynamical Systems
dc.titleNonlinear stability of stationary solutions for curvature flow with triple junction
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