教師資料查詢 | 類別: 期刊論文 | 教師: 郭忠勝 Guo, Jong-shenq (瀏覽個人網頁)

標題: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
語言英文(美國)
ISSN0036-1410
期刊性質國外
收錄於SCI;
產學合作
通訊作者Philippe Souplet
審稿制度
國別美國
公開徵稿
出版型式,紙本
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