Finite time singularity in a free boundary problem modeling MEMS

Joachim Escher (1) , Philippe Laurencot (2) , Christoph Walker (3)

1 IFAM - Institute for Applied Mathematics
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 IFAM - Institut für Angewandte Mathematik

The occurrence of a finite time singularity is shown for a free boundary problem modeling microelectromechanical systems (MEMS) when the applied voltage exceeds some value. The model involves a singular nonlocal reaction term and a nonlinear curvature term accounting for large deformations.

Mots clés: finite time singularity; MEMS; free boundary; quasilinear parabolic equation

Domaines: Equations aux dérivées partielles [math.AP]

Joachim Escher, Philippe Laurencot, Christoph Walker. Finite time singularity in a free boundary problem modeling MEMS. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2013, 351, pp.807-812. ⟨10.1016/j.crma.2013.10.004⟩. ⟨hal-00828702⟩