Kavallaris, Nikos I.2016-08-262016-08-262016-09-15Kavallaris, N. I. (2018). Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control. Mathematical Methods in the Applied Sciences, 41(3), 1074-1082. doi:10.1002/mma.41761099-147610.1002/mma.4176http://hdl.handle.net/10034/618944This is the peer reviewed version of the following article: Kavallaris, N. I. (2018). Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control. Mathematical Methods in the Applied Sciences, 41(3), 1074-1082. doi:10.1002/mma.4176, which has been published in final form at DOI: 10.1002/mma.4176. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingIn the current paper, we consider a stochastic parabolic equation which actually serves as a mathematical model describing the operation of an electrostatic actuated micro-electro-mechanical system (MEMS). 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 {\it finite-time quenching} for this SPDE, corresponding to the mechanical phenomenon of {\it touching down}, occurs. For that purpose the Kaplan's eigenfunction method adapted in the context of SPDES is employed.enhttp://creativecommons.org/licenses/by-nc-nd/4.0/Electrostatic MEMS, touchdown, quenching, stochastic semilinear partial differential equationsArticleMathematical Methods in the Applied Sciences