No Touchdown at Zero Points of the Permittivity Profile for the MEMS Problem
學年 103
學期 2
出版（發表）日期 2015-02-01
作品名稱 No Touchdown at Zero Points of the Permittivity Profile for the MEMS Problem
作品名稱（其他語言）
著者 Guo, Jong-Shenq; Philippe Souplet
單位 淡江大學數學學系
出版者 Philadelphia: Society for Industrial and Applied Mathematics
著錄名稱、卷期、頁數 SIAM Journal on Mathematical Analysis 47(1), pp.614-625
摘要 We study the quenching behavior for a semilinear heat equation arising in models of micro-electro-mechanical systems (MEMS). The problem involves a source term with a spatially dependent potential, given by the dielectric permittivity profile, and quenching corresponds to a touchdown phenomenon. It is well known that quenching does occur. We prove that touchdown cannot occur at zero points of the permittivity profile. In particular, we remove the assumption of compactness of the touchdown set, made in all previous work on the subject and whose validity is unknown in most typical cases. This answers affirmatively a conjecture made in [W. Guo, Z. Pan, and M. J. Ward, SIAM J. Appl. Math., 66 (2005), pp. 309--338] on the basis of numerical evidence. The result crucially depends on a new type I estimate of the quenching rate, that we establish. In addition we obtain some sufficient conditions for compactness of the touchdown set, without a convexity assumption on the domain. These results may be of some qualitative importance in applications to MEMS optimal design, especially for devices such as microvalves.
關鍵字
語言 en_US
ISSN 0036-1410
期刊性質 國外
收錄於 SCI
產學合作
通訊作者 Philippe Souplet
審稿制度 否
國別 USA
公開徵稿
出版型式 ,紙本
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