THE EVOLUTION OF NONLOCAL CURVATURE FLOW ARISING IN A HELE–SHAW PROBLEM

Speaker: 王小六 (东南大学)

Time: 22nd, May thursday, 9:30-11:30

Location: R1310, SIMIS
Zoom Meeting ID: 479 937 5280 (Passcode: SIMIS)

摘要：
In this talk, we consider long time behavior of a given smooth convex embedded closed curve evolving according to a nonlocal curvature flow, which arises in a Hele–Shaw problem and has a prescribed rate of change in its enclosed area A(t), i.e., dA/dt = – \beta , where \beta \in ( – \infty , \infty ). Specifically, when the enclosed area expands at any fixed rate, i.e., \beta \in ( – \infty , 0), or decreases at a fixed rate \beta \in (0, 2\pi ), 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). This is a joint work with Prof. Tsai Dong-Ho.