Finite time singularity in a free boundary problem modeling MEMS

TL;DR

This paper demonstrates the development of finite time singularities in a MEMS model with a free boundary, influenced by high voltage, nonlinear curvature, and nonlocal reaction effects.

Contribution

It introduces a new free boundary problem model for MEMS that includes singular nonlocal reactions and nonlinear curvature effects, showing finite time singularity formation.

Findings

Finite time singularity occurs when voltage exceeds a critical value.

The model incorporates nonlinear curvature and nonlocal reaction terms.

Singularity formation is proven mathematically under certain conditions.

Abstract

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.