Some recent results on a free boundary problem for microelectromechanical systems. Issue 1 (December 2014)

• Record Type: Journal Article
• Authors: Escher, Joachim; Laurençot, Philippe; Walker, Christoph
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 14:Issue 1(2014)
• Page Start: 761
• Page End: 762
• Publication Date: 2014-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201410363
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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 &amp; Co. KGaA, Weinheim)</p> </abstract>