非傅立叶热方程初态的作用
The role of the initial states for non-Fourier heat equations
摘要：
有几个模型的热传导-非傅立叶方程-在文献中是重要的各种实际问题。这些模型表现在偏微分方程中，其应用需要开发高效可靠的求解方法。在本文中，我们专注于两个非傅立叶模型的解析解，特别是麦克斯韦-Cattaneo-Vernotte和Guyer-Krumhansl方程，因为它们共享一个既定的热力学背景，并找到许多应用。虽然初始条件在许多情况下通常是空间齐次的，但实际应用可以很容易地指向这样一个简单的初始状态之外。因此，我们的目标是调查的后果，非齐次初始条件，强调的物理要求，以保持解决方案的物理容许。我们得出的计算方法确定的初始时间导数与热力学一致，避免矛盾。
英文摘要：
There are several models for heat conduction - non-Fourier equations - in the literature that are important for various practical problems. These models manifest themselves in partial differential equations, and the application of which requires developing efficient and reliable solution methods. In the present paper, we focus on the analytical solutions of two non-Fourier models, specifically on the Maxwell-Cattaneo-Vernotte and Guyer-Krumhansl equations, as they share an established thermodynamic background, and find numerous applications. Although initial conditions are usually homogeneous in space in many situations, real applications can easily point beyond such a simple initial state. Therefore, we aim to investigate the consequences of nonhomogeneous initial conditions, emphasising the physical requirements to keep the solution physically admissible. We conclude the calculations with a method for determining the initial time derivatives in consistence with thermodynamics, avoiding contradictions.
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