On a free boundary problem for the curvature flow with driving force
學年 104
學期 1
出版（發表）日期 2015-08-27
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
單位
出版者
著錄名稱、卷期、頁數 Archive for Rational Mechanics and Analysis 219(3), pp.1207-1272
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
ISSN 1432-0673
期刊性質 國外
收錄於 SCI
產學合作
通訊作者 Jong-Shenq Guo
審稿制度 是
國別 DEU
公開徵稿
出版型式 ,電子版,紙本
相關連結

機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/107128 )