Garcke, Harald and Goesswein, Michael (2021) Non-linear stability of double bubbles under surface diffusion. JOURNAL OF DIFFERENTIAL EQUATIONS, 302. pp. 617-661. ISSN 0022-0396, 1090-2732
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We consider the evolution of triple junction clusters driven by the surface diffusion flow. On the triple line we use the boundary conditions derived by Garcke and Novick-Cohen as the singular limit of a Cahn Hilliard equation with degenerated mobility. These conditions are the concurrency of the triple junction, angle conditions between the hypersurfaces, continuity of the chemical potentials and a flux-balance. For this system we show stability of its energy minimizers, i.e., standard double bubbles. The main argument relies on a Lojasiewicz-Simon gradient inequality. The proof of it differs from others works due to the fully non-linear boundary conditions and problems with the (non-local) tangential part. (c) 2021 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EQUATIONS; EVOLUTION; FLOW; Surface diffusion flow; Triple junctions; Stability analysis; Lojasiewicz-Simon gradient inequality |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 Jul 2022 05:00 |
| Last Modified: | 06 Jul 2022 05:00 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45621 |
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