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On Fourth Order PDEs Modelling Electrostatic Micro-Electronical Systems

Speaker: 
Nassif Ghoussoub
Date: 
Wed, Jul 8, 2009
Location: 
University of New South Wales, Sydney, Australia
Conference: 
1st PRIMA Congress
Abstract: 

Micro-ElectroMechanical Systems (MEMS) and Nano-ElectroMechanical Systems (NEMS) are now a well established sector of contemporary technology. A key component of such systems is the simple idealized electrostatic device consisting of a thin and deformable plate that is held fixed along its boundary TeX Embedding failed!, where TeX Embedding failed! is a bounded domain in TeX Embedding failed! The plate, which lies below another parallel rigid grounded plate (say at level TeX Embedding failed!) has its upper surface coated with a negligibly thin metallic conducting film, in such a way that if a voltage l is applied to the conducting film, it deflects towards the top plate, and if the applied voltage is increased beyond a certain critical value TeX Embedding failed!, it then proceeds to touch the grounded plate. The steady-state is then lost, and we have a snap-through at a finite time creating the so-called pull-in instability. A proposed model for the deflection is given by the evolution equation

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Now unlike the model involving only the second order Laplacian (i.e., TeX Embedding failed!), very little is known about this equation. We shall explain how, besides the above practical considerations, the model is an extremely rich source of interesting mathematical phenomena.