Fractional time differential equations as a singular limit of the Kobayashi-Warren-Carter system
arXiv (Cornell University)(2023)
摘要
This paper is concerned with a singular limit of the Kobayashi-Warren-Carter system, a phase field system modelling the evolutions of structures of grains. Under a suitable scaling, the limit system is formally derived when the interface thickness parameter tends to zero. Different from many other problems, it turns out that the limit system is a system involving fractional time derivatives, although the original system is a simple gradient flow. A rigorous derivation is given when the problem is reduced to a gradient flow of a single-well Modica-Mortola functional in a one-dimensional setting.
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关键词
fractional time,singular limit,differential equations,kobayashi-warren-carter
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