偏微分方程式セミナー(2016/10/14): Global existence of weak solution for volume preserving mean curvature flow via phase field method, 高棹 圭介 氏 (東京大学)

開催日時
2016年   10月 14日 16時 30分 ~ 2016年   10月 14日 18時 00分
場所
北海道大学理学部3号館3-309室
講演者
高棹 圭介 氏 (東京大学)
 

The Allen-Cahn equation with non-local term for the volume preserving mean curvature flow studied by Rubinstein and Sternberg is well known. However, whether the solution converges to the time global weak solution of the volume preserving mean curvature flow or not is an open problem, due to the difficulty of estimates of the Lagrange multipliers. In this talk, we consider the Allen-Cahn equation with non-local term studied by Golovaty. We show the $L^2$ estimates of the Lagrange multipliers and the convergence of the Allen-Cahn equation to the volume preserving mean curvature flow. We also give the monotonicity formula for the Allen-Cahn equation.



関連項目

研究集会・セミナー・集中講義の一覧へ