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Stability analysis for the anisotropic curve shortening flow of planar networks

Author

Listed:
  • Michael Gößwein

    (Universität Duisburg-Essen)

  • Matteo Novaga

    (Universitàdi Pisa)

  • Paola Pozzi

    (Universität Duisburg-Essen)

Abstract

In this article we consider the anisotropic curve shortening flow for a planar network of three curves which meet at a triple junction. We show that the anisotropic energy fulfills a Łojasiewicz–Simon gradient inequality from which we derive a stability result for the evolution. Precisely, we show that, for initial data which are close to the energy minimizer, the flow exists globally and converges to the minimizer.

Suggested Citation

  • Michael Gößwein & Matteo Novaga & Paola Pozzi, 2024. "Stability analysis for the anisotropic curve shortening flow of planar networks," Partial Differential Equations and Applications, Springer, vol. 5(5), pages 1-42, October.
    • Handle: RePEc:spr:pardea:v:5:y:2024:i:5:d:10.1007_s42985-024-00300-3
    DOI: 10.1007/s42985-024-00300-3
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    Keywords

    53E10; 53A04; 35A01; 46N20;
    All these keywords.

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