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Einladung zum Vortrag (Zoom) von Frau Prof. Dr. Anna Dall'Acqua (Universität Ulm) am 19.01.2022 - 14:30 Uhr im Rahmen des Forschungsseminars Analysis

[19.01.2022]

Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 19. Januar 2022, um 14:30 Uhr,

Frau Prof. Dr. Anna Dall'Acqua (Universität Ulm)

einen Vortrag zum Thema

On the elastic flow of networks.

Abstract: In the Bernoulli model of an elastic rod described by a curve the elastic energy is given by the integral over the curve of the curvature squared. Due to the behavior of the energy under scaling, one soon notices that the length of the curve should be penalized (or fixed) to find minimizers.

For this penalized energy we consider the steepest descent flow. That is, a one-parameter family of curves that changes in time in such a way that the energy decreases as fast as possible, i.e., in the direction of the $L^2$-gradient of the energy. This gives a fourth order geometric flow. For closed curves, it is well known that, starting from a smooth initial datum, the solution exists for all time and sub-converges to a critical point.

We extend this result to networks of 3-curves. We consider networks of 3-curves in $\R^{n}$, where each of the three curves is fixed at one end-point and at the other is joint to the other curves at a movable 3-junction, a three pointed star network. For this geometric evolution problem with natural boundary condition we provide a long-time existence result and a sub-convergence result
under some mild topological assumptions.

This is joint work with Chun-Chi Lin (National Taiwan Normal University) and Paola Pozzi (University of Duisburg Essen).


Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn Prof. Mugnolo (delio.mugnolo@fernuni-hagen.de) melden.

mathinf.webteam | 17.12.2021