R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Singular Limit Problem of the Allen-Cahn Equation with a 0-Neumnann Boundary Condition on Non-convex Domains
Takashi Kagaya (Kyushu University)
Abstract:
In this talk, we consider the mean curvature flow in a fixed domain and with free boundary in the boundary of the domain. For this free boundary problem, the mean curvature flow should "pop" upon tangential contact with the boundary of the domain. In order to consider "popping", we introduce a measure-theoretic weak solution to the mean curvature flow, which is called the Brakke flow.
We prove the time global existence of the free boundary Brakke flow via a singular limit problem of the Allen-Cahn equation with 0-Neumann boundary condition.