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Daily Overview |
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Gvp3: Geometric variational problems Location: A704 Session Chair: Fabian Rupp Session Chair: Christian Scharrer | |
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Existence and convergence of the area-constrained elastic flow University of Bonn, Germany
The Bernoulli model describes the bending behaviour of an elastic rod -- represented by a smooth immersed curve $\gamma: \mathbb{S}^1 \to \mathbb{R}^2$ -- in terms of its stored elastic energy. To predict this behaviour, it is classical to study the evolution of curves with fixed length moving by the negative $L^2$-gradient of the elastic energy. This talk focuses on the less-known flow subject to fixed enclosed area rather than fixed length.
While local and global existence hold for smooth initial data, establishing convergence requires a uniform bound on the length of the evolving curves. In contrast to the length-constrained flow, this bound is non-trivial. Indeed, there exist initial configurations for which the length diverges to infinity. This talk presents strategies to obtain length bounds through initial energy assumptions. | |
