动态边界条件下奇异型Kobayashi-Warren-Carter系统

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

{"title":"动态边界条件下奇异型Kobayashi-Warren-Carter系统","authors":"Ryota Nakayashiki, K. Shirakawa","doi":"10.3934/dcdss.2023162","DOIUrl":null,"url":null,"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.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"78 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kobayashi-Warren-Carter system of singular type under dynamic boundary condition\",\"authors\":\"Ryota Nakayashiki, K. Shirakawa\",\"doi\":\"10.3934/dcdss.2023162\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":48838,\"journal\":{\"name\":\"Discrete and Continuous Dynamical Systems-Series S\",\"volume\":\"78 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete and Continuous Dynamical Systems-Series S\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/dcdss.2023162\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Continuous Dynamical Systems-Series S","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/dcdss.2023162","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

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。

查看原文本刊更多论文

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

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.