Applied Analysis

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.)

2006/11/16

16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
奈良 光紀 (東京工業大学)
The large time behavior of graphical surfaces in the mean curvature flow
[ Abstract ]
We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.