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

Guo, Jong-Shenq; Hu, Bei; Wang, Chi-Jen

doi:10.1090/S0033-569X-09-01159-5

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
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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.

References

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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

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