過去の記録 ~04/13次回の予定今後の予定 04/14~

開催情報 火曜日 10:30~11:30 数理科学研究科棟(駒場) 056号室
担当者 儀我美一、石毛和弘、三竹大寿、米田剛
セミナーURL http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/
目的 首都圏の偏微分方程式、実解析の研究をさらに活発にするために本研究会を東大で開催いたします。


16:00-17:00   数理科学研究科棟(駒場) 370号室
Maximilian Moser 氏 (University of Regensburg)
Convergence of the Allen-Cahn equation with a nonlinear Robin-boundary condition to mean curvature flow with constant contact angle (English)
[ 講演概要 ]
In this talk I will present a result for the sharp interface limit of the Allen-Cahn equation with a nonlinear Robin boundary condition in a two-dimensional domain, in the situation where an interface has developed and intersects the boundary. The boundary condition is designed in such a way that one obtains as the limit problem the mean curvature flow with constant contact angle. Convergence using strong norms is shown for contact angles close to 90° and small times, when a smooth solution to the limit problem exists. For the proof the method of de Mottoni and Schatzman is used: we construct an approximate solution for the Allen-Cahn system using asymptotic expansions based on the solution to the limit problem. Then we estimate the difference of the exact and approximate solution with a spectral estimate for the linearized (at the approximate solution) Allen-Cahn operator.
This is joint work with Helmut Abels from Regensburg.