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

2023/06/27 by Yoshikazu Giga, Giga, Yoshikazu, Ayato Kubo +9 · 1 citation
Computer Science · Engineering · Materials Science · #35K20 #35Q74 #35R11 #74N99 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Metallic Glasses and Amorphous Alloys #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2306.15235

openalex publication_date 2023/06/27 · openalex created_date 2023/06/29 · openalex updated_date 2026/07/28

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.

Cited by

• Optimal Control of Pseudo-Parabolic KWC Systems for Grain Boundary Motion

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