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October 8, 2025Open Access

The vector-valued Allen-Cahn equation with potentials of high-dimensional double-wells under Robin boundary conditions

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This work shows convergence to mean curvature flow in vector-valued systems, indicating potential for broader applications.

Solutions converge locally in time to mean curvature flow with a fixed contact angle, reinforcing stability under certain conditions.
The limiting sharp-interface system includes harmonic heat flows and minimal pair conditions, essential for phase boundary analysis.
The combination of methods like relative entropy and gradient flow offers a robust framework for tackling boundary issues.
Findings extend prior analyses on vector and scalar cases, highlighting the complexity of boundary energy interplay.

Xingyu Wang (2025) studied this question.

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