Premium
Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control
Author(s) -
Kavallaris Nikos I.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4176
Subject(s) - partial differential equation , mathematics , context (archaeology) , stochastic partial differential equation , stochastic differential equation , eigenfunction , parabolic partial differential equation , quenching (fluorescence) , stochastic control , mathematical analysis , optimal control , mathematical optimization , physics , eigenvalues and eigenvectors , paleontology , quantum mechanics , fluorescence , biology
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.