期刊論文
| 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 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/103161 ) |