论文标题
在诱导硬化，存在和弱的唯一性方面，模型的熵解决方案薄弱
Weak entropy solutions to a model in induction hardening, existence and weak-strong uniqueness
论文作者
论文摘要
在本文中，我们研究了一个描述钢的诱导硬化的模型。相关系统由能量平衡，钢的不同阶段的颂歌以及潜在公式的麦克斯韦方程组成。通过合适的正则化和离散化技术显示了弱熵溶液的存在。此外，我们证明了这些解决方案的弱唯一性，即弱熵解决方案与经典溶液相吻合，只要经典的溶液具有相同的初始数据。与先前引入的弱解决方案相比，弱熵解决方案概念具有优势，例如，它允许包含具有相对于相变的较低规律性属性的自由能函数。
In this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ODE for the different phases of steel, and Maxwell's equations in a potential formulation. The existence of weak entropy solutions is shown by a suitable regularization and discretization technique. Moreover, we prove the weak-strong uniqueness of these solutions, i.e., that a weak entropy solutions coincides with a classical solution emanating form the same initial data as long as the classical one exists. The weak entropy solution concept has advantages in comparison to the previously introduced weak solutions, e.g., it allows to include free energy functions with low regularity properties corresponding to phase transitions.
