论文标题
存在于3D粒边界运动的相位模型的解决方案，该模型由正规化的1谐波流量控制
Existence of solutions to a phase-field model of 3D-grain boundary motion governed by a regularized 1-harmonic type flow
论文作者
论文摘要
在本文中，我们提出了三维Kobayashi-Warren模型中的方向变量的四元组公式，用于多晶的动力学。我们通过几个近似问题获得了约束能量功能的$ l^2 $降差下降流的解决方案。特别是，我们使用Ginzburg-Landau型方法和一些额外的正规化。通过使用非线性半群来显示近似问题的解决方案。再加上良好的A-Priori估计值，这将导致连续的段落达到极限，直到最终显示出对拟议模型的解决方案的存在。此外，我们还获得了方向变量的最大原理。
In this paper we propose a quaternion formulation for the orientation variable in the three dimensional Kobayashi--Warren model for the dynamics of polycrystals. We obtain existence of solutions to the $L^2$-gradient descent flow of the constrained energy functional via several approximating problems. In particular, we use a Ginzburg-Landau type approach and some extra regularizations. Existence of solutions to the approximating problems is shown by the use of nonlinear semigroups. Coupled with good a-priori estimates, this leads to successive passages to the limit up to finally showing existence of solutions to the proposed model. Moreover, we also obtain a maximum principle for the orientation variable.
