A stationary free boundary problem modeling electrostatic MEMS

Philippe Laurencot (1) , Christoph Walker (2)

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

A free boundary problem describing small deformations in a membrane based model of electrostatically actuated MEMS is investigated. The existence of stationary solutions is established for small voltage values. A justification of the widely studied narrow-gap model is given by showing that steady state solutions of the free boundary problem converge toward stationary solutions of the narrow-gap model when the aspect ratio of the device tends to zero.

Mots clés: MEMS; free boundary problem; small-aspect ratio limit

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurencot, Christoph Walker. A stationary free boundary problem modeling electrostatic MEMS. Archive for Rational Mechanics and Analysis, 2013, 207, pp.139--158. ⟨10.1007/s00205-012-0559-7⟩. ⟨hal-00638254⟩