题目：On a Non-local Curvature Flow Arising From the Hele-Shaw Problem
报告人： Professor Tsai Dong-Ho （中国台湾清华大学）
Abstract: We consider long time behavior of a given smooth convex embedded closed curve evolving according to a non-local curvature flow, which arises in a Hele-Shaw problem and has a prescribed rate of change in its enclosed area A (t), i.e. , where is given. Specifically, when the enclosed area expands at any fixed rate, i.e. or decreases at a fixed rate one has the round circle as the unique asymptotic shape of the evolving curves; while for a sufficiently large rate of area decrease, one can have n-fold symmetric curves (which look like regular polygons with smooth corners) as extinction shapes (self-similar solutions).
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