Finite time singularity in a MEMS model revisited
Analysis of PDEs
2016-12-20 v1
Abstract
A free boundary problem modeling a microelectromechanical system (MEMS) consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at different electrostatic potentials. It couples a second order semilinear parabolic equation for the deformation of the top plate to a Laplace equation for the electrostatic potential in the device. The validity of the model is expected to break down in finite time when the applied voltage exceeds a certain value, a finite time singularity occurring then. This result, already known for non-positive initial configurations of the top plate, is here proved for arbitrary ones and thus now includes, in particular, snap-through instabilities.
Cite
@article{arxiv.1612.05761,
title = {Finite time singularity in a MEMS model revisited},
author = {Philippe Laurençot and Christoph Walker},
journal= {arXiv preprint arXiv:1612.05761},
year = {2016}
}