# Some singular equations modeling MEMS

## TL;DR

This survey reviews recent mathematical modeling efforts for MEMS, focusing on complex models with moving boundaries and their qualitative properties, highlighting recent advances in analysis of these sophisticated systems.

## Contribution

It provides an overview of recent progress in analyzing complex MEMS models with moving boundaries, emphasizing the transition from simplified to more realistic models.

## Key findings

- Recent analysis of complex MEMS models with moving boundaries
- Progress in understanding qualitative properties of MEMS equations
- Survey of recent mathematical techniques applied to MEMS modeling

## 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.