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Volume-Preserving Mean Curvature and Willmore Flows with Line Tension

Müller, Lars (2013) Volume-Preserving Mean Curvature and Willmore Flows with Line Tension. PhD, Universität Regensburg.

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Date of publication of this fulltext: 12 Dec 2013 16:09

Abstract (English)

We show the short-time existence and uniqueness of solutions for the motion of an evolving hypersurface in contact with a solid container driven by volume-preserving Mean Curvature Flow (MCF) and line tension effect on the boundary. Difficulties arise due to the non-local nature of the resulting second order, nonlinear PDE, which will be overcome by a perturbation result from semigroup theory. In ...

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Translation of the abstract (German)

Wir zeigen die Kurzzeitexistenz und Eindeutigkeit von Lösungen für die Bewegung einer evolvierenden Hyperfläche in Kontakt mit einem festen Behälter, welche durch den volumenerhaltenden mittleren Krümmungsfluss mit Linienspannung am Rand getrieben wird. Schwierigkeiten treten durch die nicht-lokale Natur der resultierenden nichtlinearen Partiellen Differentialgleichung zweiter Ordnung auf, welche ...

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Item type:Thesis of the University of Regensburg (PhD)
Date:12 December 2013
Referee:Prof. Dr. Helmut Abels
Date of exam:28 November 2013
Institutions:Mathematics > Prof. Dr. Helmut Abels
Keywords:Mean Curvature Flow, Willmore Flow, dynamic boundary conditions, well-posedness, stability
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:29195
Owner only: item control page

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