On MEMS equation with fringing field

Authors:
Juncheng Wei and Dong Ye

Journal:
Proc. Amer. Math. Soc. **138** (2010), 1693-1699

MSC (2010):
Primary 35B45; Secondary 35J15

Published electronically:
December 30, 2009

MathSciNet review:
2587454

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the MEMS equation with fringing field

*the rupture level 1*for all . Moreover, there exists such that there are at least two solutions when ; a unique solution exists when ; and there is no solution when . This represents a dramatic change of behavior with respect to the zero fringing field case (i.e., ) and confirms the simulations in a paper by Pelesko and Driscoll as well as a paper by Lindsay and Ward.

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Additional Information

**Juncheng Wei**

Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

Email:
wei@math.cuhk.edu.hk

**Dong Ye**

Affiliation:
LMAM, UMR 7122, Université de Metz, 57045 Metz, France

Email:
dong.ye@univ-metz.fr

DOI:
https://doi.org/10.1090/S0002-9939-09-10226-5

Keywords:
MEMS,
rupture,
fringing field,
bifurcation

Received by editor(s):
August 13, 2009

Published electronically:
December 30, 2009

Additional Notes:
The research of the first author is supported by the General Research Fund from the Research Grant Council of Hong Kong

The second author is supported by the French ANR project ANR-08-BLAN-0335-01

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.