會議論文
| 學年 | 103 |
|---|---|
| 學期 | 2 |
| 發表日期 | 2015-05-19 |
| 作品名稱 | On a free boundary problem for the curvature flow with driving force |
| 作品名稱（其他語言） | |
| 著者 | Guo, Jong-shenq; Hiroshi Matano; Masahiko Shimojo; Wu, Chang-hong |
| 作品所屬單位 | |
| 出版者 | |
| 會議名稱 | International Workshop on Mathematics in the Life and Physical Science |
| 會議地點 | Beijing, China |
| 摘要 | We study a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. Our first main result concerns the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shrinking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. We also prove results on the concavity properties of solutions. One of the main tools of this paper is the intersection number principle, however in order to deal with solutions with free boundaries, we introduce what we call “the extended intersection number principle”, which turns out to be exceedingly useful in handling curves with moving endpoints. |
| 關鍵字 | Contact Angle;Curvature Flow;Travel Wave Solution;Intersection Number;Mild Solution |
| 語言 | en |
| 收錄於 | |
| 會議性質 | 國際 |
| 校內研討會地點 | 無 |
| 研討會時間 | 20150519~20150521 |
| 通訊作者 | |
| 國別 | CHN |
| 公開徵稿 | |
| 出版型式 | |
| 出處 | Archive for Rational Mechanics and Analysis 219, p.1207-1272 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/107199 ) |