Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control
Nikos I. Kavallaris · Mathematical Methods in the Applied Sciences · 2016
In the current paper, we consider a stochastic parabolic equation that actually serves as a mathematical model describing the operation of an electrostatic actuated micro‐electro‐mechanical system. We first present the derivation of the mathematical model. Then after establishing the local well posedeness of the problem, we investigate under which circumstances a finite‐time quenching for this stochastic partial differential equation, corresponding to the mechanical phenomenon of touching down, occurs. For that purpose, the Kaplan's eigenfunction method adapted in the context of stochastic partial differential equations is employed. Copyright © 2016 John Wiley & Sons, Ltd.