Stability analysis for the anisotropic curve shortening flow of planar networks

Michael Gößwein (), Matteo Novaga () and Paola Pozzi ()
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Michael Gößwein: Universität Duisburg-Essen
Matteo Novaga: Universitàdi Pisa
Paola Pozzi: Universität Duisburg-Essen

Partial Differential Equations and Applications, 2024, vol. 5, issue 5, 1-42

Abstract: 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.

Keywords: 53E10; 53A04; 35A01; 46N20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00300-3

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