Stability of stationary interfaces of binary-tree type

Ikota, Ryo; Yanagida, Eiji
April 2005
Calculus of Variations & Partial Differential Equations;Apr2005, Vol. 22 Issue 4, p375
Academic Journal
We consider the curvature-driven motion of an interface on a bounded domain that contacts with the boundary at the right angle and has triple junctions with prescribed angles. We derive a linearized system at a stationary interface, and obtain a characteristic function whose zeros correspond to the eigenvalues of the linearized operator. From the characteristic function, it is shown that the unstable dimension is not relevant to the topology of the stationary interface but depends mainly on the curvature of the boundary.


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