论文标题
Allen-Cahn型方程和Kobayashi-Warren-Carter类型的晶粒边界运动模型的耦合系统中的能量散落
Energy-dissipation in a coupled system of Allen-Cahn type equation and Kobayashi-Warren-Carter type model of grain boundary motion
论文作者
论文摘要
在本文中，我们将抛物线方程的初始边界价值问题系统视为“ $ - $ $ - $η$ - $θ$模型”的广义版本，该版本由Kobayashi [16]提出。该系统是一个耦合系统：allen-cahn类型方程，如（1.1），具有给定的温度源；以及晶界运动的相位模型，称为“ kobayashi-warren型模型”。该研究的重点是一种特殊的解决方案，称为能量散文溶液，即在及时重现管理能量的能量散引力。在合适的假设下，两个主要定理，与：能量散文解决方案的存在；和大型行为；将作为本文的结果证明。
In this paper, we consider a system of initial boundary value problems for parabolic equations, as a generalized version of the "$ ϕ$-$ η$-$ θ$ model" of grain boundary motion, proposed by Kobayashi [16]. The system is a coupled system of: an Allen--Cahn type equation as in (1.1) with a given temperature source; and a phase-field model of grain boundary motion, known as "Kobayashi--Warren--Carter type model". The focus of the study is on a special kind of solution, called energy-dissipative solution, which is to reproduce the energy-dissipation of the governing energy in time. Under suitable assumptions, two Main Theorems, concerned with: the existence of energy-dissipative solution; and the large-time behavior; will be demonstrated as the results of this paper.
