论文标题
初始状态对于非倍级热方程的作用
The role of the initial states for non-Fourier heat equations
论文作者
论文摘要
在文献中，有几种用于热传导的模型 - 非峰等方程 - 对于各种实际问题很重要。这些模型以部分微分方程表现出来，其应用需要开发高效可靠的解决方案方法。在本文中，我们关注了两个非呼吸模型的分析解决方案，特别是Maxwell-Cattaneo-Vernotte和Guyer-Krumhansl方程，它们具有建立的热力学背景，并找到了许多应用。尽管在许多情况下的空间中，初始条件通常是同质的，但实际应用可以轻松地指向如此简单的初始状态。因此，我们旨在调查非均匀初始条件的后果，强调物理要求，以保持溶液在物理上可以接受。我们以一种与热力学一致的初始时间导数来确定初始时间导数的方法，避免了矛盾。
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.
