论文标题
基于微毛平衡的非等温cahn-hilliard模型
On a non-isothermal Cahn-Hilliard model based on a microforce balance
论文作者
论文摘要
本文涉及基于微生物平衡的非等温Cahn-Hilliard模型。该模型是由M. Gurtin的两级方法从热力学的两个基本定律开始得出的。由于绝对温度倾向于零和无穷大，因此对热通量的行为进行了主要的工作假设。考虑了合适的金茨堡 - 陆自由能。通过得出合适的先验估计值并显示出近似解决方案家族的顺序稳定性，证明了与熵公式相关的初始有限价值问题的全球及时存在，并且与模型的弱公式相关。最后，关于可能与系统可用的A-Priori估计值兼容的可能的近似方案，给出了一些亮点。
This paper is concerned with a non-isothermal Cahn-Hilliard model based on a microforce balance. The model was derived by A. Miranville and G. Schimperna starting from the two fundamental laws of Thermodynamics, following M. Gurtin's two-scale approach. The main working assumptions are made on the behaviour of the heat flux as the absolute temperature tends to zero and to infinity. A suitable Ginzburg-Landau free energy is considered. Global-in-time existence for the initial-boundary value problem associated to the entropy formulation and, in a subcase, also to the weak formulation of the model is proved by deriving suitable a priori estimates and showing weak sequential stability of families of approximating solutions. At last, some highlights are given regarding a possible approximation scheme compatible with the a-priori estimates available for the system.
