A nonlocal quenching problem arising in a micro-electro mechanical system

Authors:
Jong-Shenq Guo, Bei Hu and Chi-Jen Wang

Journal:
Quart. Appl. Math. **67** (2009), 725-734

MSC (2000):
Primary 35K60, 35Q72, 34B18

DOI:
https://doi.org/10.1090/S0033-569X-09-01159-5

Published electronically:
May 14, 2009

MathSciNet review:
2588232

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study a nonlocal parabolic problem arising in the study of a micro-electro mechanical system. The nonlocal nonlinearity involved is related to an integral over the spatial domain. We first give the structure of stationary solutions. Then we derive the convergence of a global (in time) solution to the maximal solution as the time tends to infinity. Finally, we provide some quenching criteria.

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Additional Information

**Jong-Shenq Guo**

Affiliation:
Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan; and Taida Institute of Mathematical Sciences, National Taiwan University, 1, S-4, Roosevelt Road, Taipei 10617 Taiwan

**Bei Hu**

Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

**Chi-Jen Wang**

Affiliation:
Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan

DOI:
https://doi.org/10.1090/S0033-569X-09-01159-5

Keywords:
Quenching,
nonlocal parabolic problem,
micro-electro mechanical system

Received by editor(s):
July 23, 2008

Published electronically:
May 14, 2009

Additional Notes:
The first author was partially supported by the National Science Council of the Republic of China under the grant NSC 96-2119-M-003-001.

Article copyright:
© Copyright 2009
Brown University