Some recent results on a free boundary problem for microelectromechanical systems
Joachim Escher, Philippe Laurençot, Christoph Walker · PAMM · 2014
Abstract 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)