Impacts of noise on quenching of some models arising in MEMS technology

TL;DR

This paper investigates how stochastic noise influences the quenching behavior in mathematical models of MEMS devices, providing existence results, probabilistic estimates, and numerical analysis of singularities.

Contribution

It introduces a stochastic parabolic model for MEMS, derives quenching conditions, and offers probabilistic and numerical insights into singularity formation.

Findings

Quenching can occur under stochastic fluctuations in MEMS models.

Probabilistic estimates of quenching time are provided.

Numerical simulations support theoretical results.

Abstract

In the current work we study a stochastic parabolic problem. The underlying problem is actually motivated by the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device in the case of random fluctuations of the potential difference controlling the device. We first present the mathematical model and then we deduce some local existence results. Next for some particular versions of the model, regarding its boundary conditions, we derive quenching results as well as estimations of the probability for such singularity to occur. Additional numerical study of the problem in one dimension follows, investigating the problem further with respect to its quenching behaviour.