论文标题
Guyer-Krumhansl热方程的数学分析和数值模拟
Mathematical analysis and numerical simulation of the Guyer-Krumhansl heat equation
论文作者
论文摘要
Guyer-Krumhansl热方程在低温和室温传导问题中都具有许多重要的实际应用。近年来，事实证明，Guyer-Krumhansl模型可以有效地描述宏观异质材料的热行为。因此，Guyer-Krumhansl方程是有前途的候选人成为工程学的下一个标准模型。但是，为了支持Guyer-Krumhansl方程式对工程实践的介绍，必须对其数学属性进行彻底研究和理解。在本文中，我们显示了该特定热方程的基本结构，重点是与傅立叶热方程相比{获得$（τ_{q}，μ^{2}）\ rightArrow（0,0,0）$}时的差异。此外，我们证明了特定的，实际上显着的初始和边界价值问题的良好性。还使用有限的差异方法在离散空间中研究了解决方案的稳定性。
The Guyer-Krumhansl heat equation has numerous important practical applications in both low-temperature and room temperature heat conduction problems. In recent years, it turned out that the Guyer-Krumhansl model can effectively describe the thermal behaviour of macroscale heterogeneous materials. Thus, the Guyer-Krumhansl equation is a promising candidate to be the next standard model in engineering. However, to support the Guyer-Krumhansl equation's introduction into the engineering practice, its mathematical properties must be thoroughly investigated and understood. In the present paper, we show the basic structure of this particular heat equation, focusing on the differences in comparison to the Fourier heat equation {obtained when $(τ_{q}, μ^{2})\rightarrow (0,0)$}. Additionally, we prove the well-posedness of a particular, practically significant initial and boundary value problem. The stability of the solution is also investigated in the discrete space using a finite difference approach.
