Gößwein, Michael ; Menzel, Julia ; Pluda, Alessandra
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications |
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| Verlag: | EUROPEAN MATHEMATICAL SOC-EMS |
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| Ort der Veröffentlichung: | BERLIN |
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| Band: | 25 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 1 |
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| Seitenbereich: | S. 109-154 |
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| Datum: | 2022 |
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| Institutionen: | Mathematik > Prof. Dr. Helmut Abels |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.4171/IFB/477 | DOI |
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| Stichwörter / Keywords: | PARABOLIC EQUATIONS; BOUNDARY; CURVES; FLOW; SURFACES; EVOLUTION; Networks; motion by curvature; local existence and uniqueness; parabolic regularisation; non-linear boundary conditions; long-time existence |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 75863 |
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Zusammenfassung
We prove existence and uniqueness of the motion by curvature of networks with triple junctions in R-d when the initial datum is of class W-p(2-2/p) and the unit tangent vectors to the concurring curves form angles of 120 degrees. Moreover, we investigate the regularisation effect due to the parabolic nature of the system. An application of the well-posedness is a new proof and a generalisation of ...
Zusammenfassung
We prove existence and uniqueness of the motion by curvature of networks with triple junctions in R-d when the initial datum is of class W-p(2-2/p) and the unit tangent vectors to the concurring curves form angles of 120 degrees. Moreover, we investigate the regularisation effect due to the parabolic nature of the system. An application of the well-posedness is a new proof and a generalisation of the long-time behaviour result derived by Mantegazza et al. in 2004. Our study is motivated by an open question proposed in the 2016 survey from Mantegazza et al.: does there exist a unique solution of the motion by curvature of networks with initial datum being a regular network of class C-2? We give a positive answer.
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