Some singular equations modeling MEMS

Abstract

In the past fifteen years mathematical models for microelectromechanical systems (MEMS) have been the subject of several studies, in particular due to the interesting qualitative properties they feature. Still most research is devoted to an illustrative, but simplified model which is deduced from a more complex model when the aspect ratio of the device vanishes, the so-called vanishing (or small) aspect ratio model. The analysis of the aforementioned complex model involving a moving boundary has started only recently and an outlook of the results obtained so far in this direction is provided in this survey.

References in corpus (8)

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Cited by in corpus (9)

• Singular Behavior of an Electrostatic--Elastic Membrane System with an External Pressure
• Shape derivative of the Dirichlet energy for a transmission problem
• Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems
• Quenching for a semi-linear wave equation for MEMS
• Wellposedness of a nonlinear parabolic-dispersive coupled system modelling MEMS
• Wellposedness of an elliptic-dispersive coupled system for MEMS
• Existence and uniqueness for a coupled parabolic-hyperbolic model of MEMS
• Finite time singularity in a MEMS model revisited
• On a Free Boundary Model for Three-Dimensional MEMS with a Hinged Top Plate I: Stationary Case