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PDE Real Analysis Seminar
Seminar information archive ～04/26｜Next seminar｜Future seminars 04/27～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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2020/02/28
16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)
Maximilian Moser (University of Regensburg)
Convergence of the Allen-Cahn equation with a nonlinear Robin-boundary condition to mean curvature flow with constant contact angle (English)
Maximilian Moser (University of Regensburg)
Convergence of the Allen-Cahn equation with a nonlinear Robin-boundary condition to mean curvature flow with constant contact angle (English)
[ Abstract ]
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.
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.
