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arXiv · 1210.0231

Plateau angle conditions for the vector-valued Allen-Cahn equation

Nicholas D. Alikakos·Panagiotis Antonopoulos·Apostolos Damialis
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Abstract

Under proper hypotheses, we rigorously derive the Plateau angle conditions at triple junctions of diffused interfaces in three dimensions, starting from the vector-valued Allen-Cahn equation with a triple-well potential. Our derivation is based on an application of the divergence theorem using the divergence-free form of the equation via an associated stress tensor.

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Nicholas D. Alikakos, Panagiotis Antonopoulos, Apostolos Damialis. 2012-09-30. Plateau angle conditions for the vector-valued Allen-Cahn equation. https://doi.org/10.1137/120893586

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