English

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 L1L^1 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}
}
R2 v1 2026-06-23T03:12:14.629Z