Tuesday Seminar of Analysis

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Date, time & place Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.)
Organizer(s) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

2015/05/12

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Keisuke Takasao (Graduate School of Mathematical Sciences, the University of Tokyo)
Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow (Japanese)
[ Abstract ]
In this talk we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott studied the asymptotic behavior of the solution of the Allen-Cahn equation with constraint. They proved that the zero level set of the solution converges to the classical solution of the mean curvature flow under the suitable conditions on initial data. In 1993, Ilmanen proved the existence of the mean curvature flow via the Allen-Cahn equation without constraint in the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation with constraint.