偏微分方程式セミナー (2014/06/30):The singular limit of the Allen-Cahn equation with Neumann boundary conditions, 水野将司氏 (日本大学)

開催日時
2014年   6月 30日 16時 30分 ~ 2014年   6月 30日 17時 30分
場所
北海道大学理学部3号館3-309室
講演者
水野将司氏(日本大学理工学部)
 
We study a singular limit of the Allen-Cahn equation
with Neumann boundary condtion. From the singular limit of the
solution of the Allen-Cahn equation in whole space, Ilmanen,
Tonegawa-Takasao derived the existence of a measure theoretical
solution of the mean curvature flow(the Brakke flow). Since the
gradint of the solution of the Allen-Cahn equation approximates the
measure theoretical normal vector of the Brakke flow, one may
heuristically expect that the Brakke flow obtained by our singular
limit insetersects the boundary with 90 degree angle. We discuss the
boundary behavior of the solution of our singular limit and the
formulation of the boundary condition for the Brakke flow.
This talk is based on a joint work with Yoshihiro Tonegawa.


関連項目

研究集会・セミナー・集中講義の一覧へ