Seminar 27/4/18: On mathematical models for microelectromechanical systems

On mathematical models for microelectromechanical systems
Prof Joachim Escher
Leibniz University Hannover
Friday 27 April 2018
1pm, Blue Room, 4th floor, Main Building, DIT Kevin Street

Abstract:

A review of some recent results on mathematical models for microelectromechanical systems with general permittivity profile will be presented. These models consist of a quasilinear parabolic evolution problem for the displacement of an elastic membrane coupled with an elliptic moving boundary problem that determines the electrostatic potential in the region occupied by the elastic membrane and a rigid ground plate.

Local well-posedness, global existence, the occurrence of finite-time singularities, and convergence of solutions to those of the so-called small-aspect ratio model, respectively, are addressed. Furthermore, a topic is addressed that is of note not till non-constant permittivity profiles are taken into account — the direction of the membrane's deflection or, in mathematical parlance, the sign of the solution to the evolution problem.