Touchdown is the only finite time singularity in a three-dimensional MEMS model
Analysis of PDEs
2018-07-25 v1
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 by the bi-Laplacian with clamped boundary conditions.
Cite
@article{arxiv.1807.09017,
title = {Touchdown is the only finite time singularity in a three-dimensional MEMS model},
author = {Philippe Laurençot and Christoph Walker},
journal= {arXiv preprint arXiv:1807.09017},
year = {2018}
}