Quarterly of Applied Mathematics

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

Author(s): Jong-Shenq Guo; Bei Hu; Chi-Jen Wang
Journal: Quart. Appl. Math. 67 (2009), 725-734.
MSC (2000): Primary 35K60, 35Q72, 34B18
Posted: May 14, 2009
MathSciNet review: 2588232
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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
PII: S0033-569X-09-01159-5
Keywords: Quenching, nonlocal parabolic problem, micro-electro mechanical system
Received by editor(s): July 23, 2008
Posted: 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.
Copyright of article: Copyright 2009, Brown University

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