A free boundary problem modeling electrostatic MEMS: II. nonlinear bending effects

Philippe Laurencot (1) , Christoph Walker (2)

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

Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically conductive elastic membrane suspended above a fixed ground plate together with the electrostatic potential in the free domain between the membrane and the fixed ground plate. The electrostatic potential is harmonic in that domain and its values are held fixed along the membrane and the ground plate. The equation for the membrane deflection is a parabolic quasilinear fourth-order equation, which is coupled to the gradient trace of the electrostatic potential on the membrane.

Mots clés: MEMS; free boundary problem; curvature; well-posedness; bending

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurencot, Christoph Walker. A free boundary problem modeling electrostatic MEMS: II. nonlinear bending effects. Mathematical Models and Methods in Applied Sciences, 2014, 24 (13), pp.2549--2568. ⟨10.1142/S0218202514500298⟩. ⟨hal-00861781⟩