On a free boundary problem for the curvature flow with driving force

doi:10.1007/s00205-015-0920-8

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 會議論文 > Item 987654321/107199

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題名:	On a free boundary problem for the curvature flow with driving force
作者:	Guo, Jong-shenq;Hiroshi Matano;Masahiko Shimojo;Wu, Chang-hong
關鍵詞:	Contact Angle;Curvature Flow;Travel Wave Solution;Intersection Number;Mild Solution
日期:	2015-05-19
上傳時間:	2016-08-18 13:34:04 (UTC+8)
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.
關聯:	Archive for Rational Mechanics and Analysis 219,　p.1207-1272
DOI:	10.1007/s00205-015-0920-8
顯示於類別:	[數學學系暨研究所] 會議論文

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