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Stability of stationary interfaces of binary-tree type

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Abstract.

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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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, 812-8581, Fukuoka, Japan

    Ryo Ikota

  2. Mathematical Institute, Tohoku University, 980-8578, Sendai, Japan

    Eiji Yanagida

Authors
  1. Ryo Ikota
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  2. Eiji Yanagida
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Correspondence to Ryo Ikota.

Additional information

Received: 8 December 2003, Accepted: 5 April 2004, Published online: 16 July 2004

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Ikota, R., Yanagida, E. Stability of stationary interfaces of binary-tree type. Calc. Var. 22, 375–389 (2004). https://doi.org/10.1007/s00526-004-0281-x

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  • DOI: https://doi.org/10.1007/s00526-004-0281-x

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