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Some recent results on a free boundary problem for microelectromechanical systems
Author(s) -
Escher Joachim,
Laurençot Philippe,
Walker Christoph
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410363
Subject(s) - nonlinear system , free boundary problem , boundary value problem , boundary (topology) , stationary solution , mathematics , mathematical analysis , physics , quantum mechanics
The mathematical modeling of idealized microelectromechanical systems leads to a nonlinear singular elliptic‐parabolic free boundary problem involving non‐smooth domains and depending on a parameter λ reflecting the applied voltage across the device. Recent results derived in [1,4] are presented which confirm physically important and expected features: For small λ there is (at least) one stable stationary solution and solutions to the evolution equation exist globally in time, while for large λ no stationary solution exists and the evolution equation has no global solution. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)