Display Abstract

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

Name Masahiko Shimojo
Country Japan
Email shimojo@xmath.ous.ac.jp
Co-Author(s) Jong-Shenq Guo, Hiroshi Matano, Chang-Hong Wu
Submit Time 2014-02-18 02:39:28
Special Session 12: Complexity in reaction-diffusion systems
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 shriknking 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.