We provide the first general result for the asymptotics of the area preserving mean curvature flow in two dimensions showing that flat flow solutions, starting from any bounded set of finite perimeter, converge with exponential rate to a finite union of equally sized disjoint disks. A similar result is established also for the periodic two-phase Mullins-Sekerka flow.
The asymptotics of the area-preserving mean curvature and the Mullins–Sekerka flow in two dimensions / Julin, V.; Morini, M.; Ponsiglione, M.; Spadaro, E.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 387:3-4(2023), pp. 1969-1999. [10.1007/s00208-022-02497-3]
The asymptotics of the area-preserving mean curvature and the Mullins–Sekerka flow in two dimensions
Ponsiglione M.;Spadaro E.
2023
Abstract
We provide the first general result for the asymptotics of the area preserving mean curvature flow in two dimensions showing that flat flow solutions, starting from any bounded set of finite perimeter, converge with exponential rate to a finite union of equally sized disjoint disks. A similar result is established also for the periodic two-phase Mullins-Sekerka flow.| File | Dimensione | Formato | |
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Julin_postprint_The-asymptotic-of-the-area-preserving_2023.pdf
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