Touchdown is the only finite time singularity in a three-dimensional MEMS model

Philippe Laurençot; Christoph Walker

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arXiv · 1807.09017

Touchdown is the only finite time singularity in a three-dimensional MEMS model

Philippe Laurençot·Christoph Walker

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Abstract

Touchdown is shown to be the only possible finite time singularity that may take place in a free boundary problem modeling a three-dimensional microelectromechanical system. The proof relies on the energy structure of the problem and uses smoothing effects of the semigroup generated in $L^1$ by the bi-Laplacian with clamped boundary conditions.

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Philippe Laurençot, Christoph Walker. 2018-07-24. Touchdown is the only finite time singularity in a three-dimensional MEMS model. https://arxiv.org/abs/1807.09017

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