FINITE TIME SINGULARITY IN A MEMS MODEL REVISITED

Philippe Laurençot (1) , Christoph Walker (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IFAM - Institut für Angewandte Mathematik

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.

Mots clés: MEMS; free boundary problem; Finite time singularity

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurençot, Christoph Walker. FINITE TIME SINGULARITY IN A MEMS MODEL REVISITED. Zeitschrift für Analysis und ihre Anwendungen, 2018, 37, pp.209--219. ⟨10.4171/ZAA/1610⟩. ⟨hal-01417149⟩