The heat equation, based on Fourier’s law, is commonly used for description of heat conduction. However, Fourier’s law is valid under the assumption of local thermodynamic equilibrium, which is violated in very small dimensions and short timescales, and at low temperatures. In the paper Kovács and Ván (Int J Heat Mass Transf 83:613–620, 2015), a ballistic-conductive (BC) model of heat conduction was developed. In this paper, we study the behavior of solutions to an initial value problem in 1D in the framework of the linearized BC model. As a result of the study, an unphysical effect has been found when part of the initial thermal energy does not spread anywhere.

基于傅里叶定律的热方程通常用于描述热传导。然而，傅里叶定律在局部热力学平衡的假设下是有效的，但在非常小的尺寸、短的时间尺度和低温下，局部热力学平衡会被违反。在 Kovács 和 Ván 的论文（Int J Heat Mass Transf 83:613–620, 2015）中，开发了热传导的弹道传导 (BC) 模型。在本文中，我们研究线性化 BC 模型框架中一维初始值问题的解的行为。研究结果发现，当部分初始热能没有扩散到任何地方时，就会产生非物理效应。