NCKU Math Colloquium / RCTS Seminar
|TITLE||On a Free Boundary Problem for the Curvature Flow Eith Driving Force|
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 xed contact angles. Our rst main result concerns the classication 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.|
This talk is based on a joint work with Hiroshi Matano, Masahiki Shimojo, and Chang-Hong Wu.