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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。
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.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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