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

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 會議論文 > Item 987654321/99678

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题名:	On a free boundary problem for the curvature flow with driving force
作者:	Guo, Jong-Shenq
贡献者:	淡江大學數學學系
日期:	2013-10-23
上传时间:	2014-12-09 15:40:05 (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.
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