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arXiv · 2306.15235

Fractional time differential equations as a singular limit of the Kobayashi-Warren-Carter system

Yoshikazu Giga·Ayato Kubo·Hirotoshi Kuroda·Jun Okamoto·Koya Sakakibara·Masaaki Uesaka
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Abstract

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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Yoshikazu Giga, Ayato Kubo, Hirotoshi Kuroda, Jun Okamoto, Koya Sakakibara, Masaaki Uesaka. 2023-06-27. Fractional time differential equations as a singular limit of the Kobayashi-Warren-Carter system. https://arxiv.org/abs/2306.15235

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