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

標題:On a free boundary problem for the curvature flow with driving force
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Jong-Shenq Guo; Hiroshi Matano; Masahiko Shimojo; Chang-Hong Wu
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Renmin University of China, 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
語言英文
收錄於
會議性質國際
校內研討會地點
研討會時間20150519~20150521
通訊作者
國別中國
公開徵稿
出版型式
出處Archive for Rational Mechanics and Analysis 219, pp.1207-1272
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