Kobayashi-Warren-Carter system of singular type under dynamic boundary condition

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-08-17 DOI:10.3934/dcdss.2023162

Ryota Nakayashiki, K. Shirakawa

引用次数: 0

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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动态边界条件下奇异型Kobayashi-Warren-Carter系统

在本文中，我们考虑一个耦合系统，称为Kobayashi- Warren- Carter系统，简称为KWC系统。KWC系统由Allen—Cahn型方程和奇异扩散方程组成，由[Kobayashi et al .， Phys]提出。作为晶界运动可能的数学模型[D]， 140, 141—150(2000)。本工作的重点是在我们的KWC系统中施加的动态边界条件，而数学上的兴趣处于一种冲突的局面:动态边界条件中包含的传输条件的连续性;以及由奇异扩散方程引起的不连续。在此基础上，我们将证明具有能量耗散的KWC系统解的存在性的主要定理。此外，作为子结果，我们将证明一个关键引理，即对冲突情况给出一定的数学解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete and Continuous Dynamical Systems-Series S MATHEMATICS, APPLIED-

CiteScore

3.70

自引率

5.60%

发文量

177

期刊介绍： Series S of Discrete and Continuous Dynamical Systems only publishes theme issues. Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDS-S is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.