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arXiv:1403.5624 [math.AP]AbstractReferencesReviewsResources

Convergence of the Allen-Cahn equation with Neumann boundary conditions

Masashi Mizuno, Yoshihiro Tonegawa

Published 2014-03-22, updated 2014-09-17Version 4

We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke's mean curvature flow with a generalized right angle condition on the boundary.

Comments: 26 pages, 1 figure
Categories: math.AP, math.DG
Subjects: 28A75, 35K20, 53C44
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