ABSTRACT
This paper proposes a comprehensive framework for studying minimizing solutions of Allen-Cahn systems on curved domains, addressing challenges from interfacial dynamics and ambient curvature.
PAPER · PDF
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Key findings
Develops a variational theory for minimizing solutions on curved domains.
Proposes a surface finite element discretization maintaining energy stability and discrete maximum principles.
Formulates an experimental validation plan with systematic numerical experiments on benchmark geometries.
Limitations & open questions
Further research needed to fully understand behavior near geometric singularities.