English  |  正體中文  |  简体中文  |  全文筆數/總筆數 : 49378/84106 (59%)
造訪人次 : 7364293      線上人數 : 67
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library & TKU Library IR team.
搜尋範圍 查詢小技巧:
  • 您可在西文檢索詞彙前後加上"雙引號",以獲取較精準的檢索結果
  • 若欲以作者姓名搜尋,建議至進階搜尋限定作者欄位,可獲得較完整資料
  • 進階搜尋
    請使用永久網址來引用或連結此文件: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/103161

    題名: No Touchdown at Zero Points of the Permittivity Profile for the MEMS Problem
    作者: Guo, Jong-Shenq;Philippe Souplet
    貢獻者: 淡江大學數學學系
    日期: 2015-02
    上傳時間: 2015-05-20 07:01:32 (UTC+8)
    出版者: Philadelphia: Society for Industrial and Applied Mathematics
    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.
    關聯: SIAM Journal on Mathematical Analysis 47(1), pp.614-625
    DOI: 10.1137/140970070
    顯示於類別:[數學學系暨研究所] 期刊論文


    檔案 描述 大小格式瀏覽次數
    1502sima.pdf199KbAdobe PDF223檢視/開啟



    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library & TKU Library IR teams. Copyright ©   - 回饋