晶粒长大动力学模型
A Kinetic Model for Grain Growth
摘要：
我们提供了一个适定性分析的动力学模型引入的Fradkov是基于冯诺依曼-穆林斯定律的晶粒生长。该模型由无限多个输运方程组成，具有三对角耦合模型，用于模拟晶粒结构的拓扑变化。该动力学模型的自洽性是通过引入耦合权重得到的非线性非局部方程组实现的。我们证明了有限维系统的近似解的存在性。传递到极限的关键因素是合适的超解，总质量的下限，以及确保在有限时间内没有质量被传递到无穷大的紧密性估计。
英文摘要：
We provide a well-posedness analysis of a kinetic model for grain growth introduced by Fradkov which is based on the von Neumann-Mullins law. The model consists of an infinite number of transport equations with a tri-diagonal coupling modelling topological changes in the grain configuration. Self-consistency of this kinetic model is achieved by introducing a coupling weight which leads to a nonlinear and nonlocal system of equations. We prove existence of solutions by approximation with finite dimensional systems. Key ingredients in passing to the limit are suitable super-solutions, a bound from below on the total mass, and a tightness estimate which ensures that no mass is transported to infinity in finite time.
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