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arXiv · 2308.08770

Kobayashi-Warren-Carter System of Singular Type under Dynamic Boundary Condition

Ryota Nakayashiki·Ken Shirakawa
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Abstract

In this paper, we consider a coupled system, known as Kobayashi--Warren--Carter system, abbreviated as the KWC system. KWC system consists of an Allen--Cahn type equation and a singular diffusion equation, and it was proposed by [Kobayashi et al, Phys. D, 140, 141--150 (2000)] as a possible mathematical model of grain boundary motion. The focus of this work is on the dynamic boundary condition imposed in our KWC system, and the mathematical interest is in a conflicting situation between: the continuity of the transmission condition included in the dynamic boundary condition; and the discontinuity encouraged by the singular diffusion equation. On this basis, we will prove the Main Theorem concerned with the existence of solution to our KWC system with energy-dissipation. Additionally, as a sub-result, we will prove a key-lemma that is to give a certain mathematical interpretation for the conflicting situation.

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Ryota Nakayashiki, Ken Shirakawa. 2023-08-17. Kobayashi-Warren-Carter System of Singular Type under Dynamic Boundary Condition. https://arxiv.org/abs/2308.08770

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