Kobayashi-Warren-Carter System of Singular Type under Dynamic Boundary Condition
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.
Keywords
Cite
@article{arxiv.2308.08770,
title = {Kobayashi-Warren-Carter System of Singular Type under Dynamic Boundary Condition},
author = {Ryota Nakayashiki and Ken Shirakawa},
journal= {arXiv preprint arXiv:2308.08770},
year = {2023}
}
Comments
43 pages