Diana, Antonia (2024) The Surface Diffusion Flow: Long–Time Behaviour and Asymptotic Stability. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | The Surface Diffusion Flow: Long–Time Behaviour and Asymptotic Stability |
| Autori: | Autore Email Diana, Antonia antonia.diana@unina.it |
| Data: | 2024 |
| Numero di pagine: | 109 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dottorato: | Mathematical and physical sciences for advanced materials and technologies |
| Ciclo di dottorato: | 36 |
| Coordinatore del Corso di dottorato: | nome email Fusco, Nicola n.fusco@unina.it |
| Tutor: | nome email Mantegazza, Carlo [non definito] Pluda, Alessandra [non definito] |
| Data: | 2024 |
| Numero di pagine: | 109 |
| Parole chiave: | Geometric flow, area functional, stable critical set, surface diffusion flow, global existence, stability |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica |
| Depositato il: | 23 Ott 2025 06:35 |
| Ultima modifica: | 12 Ago 2026 05:38 |
| URI: | https://www.fedoa.unina.it/id/eprint/16913 |
Abstract
We study the global existence and stability of surface diffusion flow (the normal velocity is given by the Laplacian of the mean curvature) of smooth boundaries of subsets of the n-dimensional flat torus. More precisely, using two different approaches, we show that if a smooth set is "close enough" to a strictly stable critical set for the Area functional under a volume constraint, then the surface diffusion flow of its boundary hypersurface exists for all time and asymptotically converges to the boundary of a "translated" of the critical set.
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