A constrained model for MEMS with varying dielectric properties

Philippe Laurencot (1) , Christoph Walker (2)

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

A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a breakdown of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.

Mots clés: parabolic variational inequality; obstacle problem; MEMS; well-posedness; large time behavior

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurencot, Christoph Walker. A constrained model for MEMS with varying dielectric properties. Journal of Elliptic and Parabolic Equations, 2017, 3, pp.15--51. ⟨10.1007/s41808-017-0003-0⟩. ⟨hal-01560805⟩